Corresponding Author. The result is based on four concepts: prediction via Taylor series expansion, receding horizon control, control constraints (within the moving horizon time frame) and optimisation. A general framework for extending H–infinity control to nonlinear systems. As a result, an optimal generalised predictive control law is presented in a closed form, which turns out to be a time invariant nonlinear state feedback control law. Chapter 3 is in some sense the heart of the book, introducing, explaining, and applying Pontryagin’s Maximum Principle. Optimal control of nonlinear systems is one of the most active subjects in control theory. Under robust H∞ control strategy, the dynamic response of HTGS with SLHT is rapid and sensitive. For simplicity, the case with only iteration-varying reference is first considered, where the asymptotic stability and monotone convergence based ILC design methods are both presented by using the 2-D analysis approach. In this work, the tracking problem of switched non-affine nonlinear systems with output constraints is transformed into the stabilization problem of switched unconstrained affine systems. A general framework for extending H–infinity control to nonlinear systems. Optimal control of nonlinear systems is one of the most active subjects in control theory. Nonlinear and Optimal Control Systems: Vincent, Thomas L., Grantham, Walter J.: Amazon.sg: Books The paper is organized as follows. (2010) and Kim and Rew (2013) for continuous-time and discrete-time linear systems, respectively. Abstract: This paper studies the online adaptive optimal controller design for a class of nonlinear systems through a novel policy iteration (PI) algorithm. Control problems for systems governed by ordinary (or partial) differential equations arise in many applications, e.g., in astronautics, aeronautics, robotics, and economics. The effectiveness and superiorities of the proposed composite control scheme are demonstrated by numerical simulations. The optimal control (Pontryagin's) minimum principle is developed and then applied to optimal control problems and the design of optimal controllers. The proposed methodology iteratively updates the control policy online by using the state and input information without identifying the system dynamics. To this end, Lu (1995), Soroush and Soroush (1997) and Siller-Alcala (1998) limit the control order to be zero, that is, to limit the control effort to be a constant in the predictive interval. It is shown that the closed-loop dynamics under this nonlinear predictive controller explicitly depend on design parameters (prediction time and control order). In 1994 he was awarded the Honeywell International Medal by the Institute of Measurement and Control. Nonlinear Industrial Control Systems is valuable to engineers in industry dealing with actual nonlinear systems. Get Free Optimal Control Of Nonlinear Processes Textbook and unlimited access to our library by … He was involved in founding the Centre for Systems and Control — a cross-departmental research grouping at Glasgow with about 12 full time academic staff including four professors. In order to avoid the numerical computation difficulties in optimisation, an analytical solution to a set of nonlinear equations arising in optimisation is derived. One problem is a large computational delay and the other problem is that global minimum may not be achieved, or even worse a local minimum cannot be achieved due to time limitation in each optimisation cycle. Optimal Control of Nonlinear Continuous-Time Systems in Strict-Feedback Form Abstract: This paper proposes a novel optimal tracking control scheme for nonlinear continuous-time systems in strict-feedback form with uncertain dynamics. Programming, Discretization, Dynamical Control Systems. There is special emphasis on the fundamental topics of stability, controllability, and optimality, and on the corresponding geometry associated with these topics. Inequality and equality constrained minimization Outline . G. Zweigle, V. Venkatasubramanian, "Model Prediction Based Transient Stability Control", IEEE T&D Conference, May 7-10, 2012. in the EU. Pages 111-131. This work is focused on the iterative learning control (ILC) design for linear discrete-time systems with iteration-varying factors, including reference, initial state, and exogenous disturbances. 7879-7903, Nonlinear Analysis: Hybrid Systems, Volume 24, 2017, pp. Learn more about function, nonlinear, optimisation, optimal control, optimization These adaptive parameters in the proposed control scheme are derived using the function approximation technique and a priori knowledge of the signs of control gain functions is not required. The existence condition of the promising algorithm has been established but is not straightforward to check. An optimal control strategy for nonlinear stochastic vi- bration using a piezoelectric stack inertial actuator has been proposed in this paper. Lastly, the simulation results show the high efficiency and precision of the proposed control method. Nevertheless, a number of alternative (suboptimal) approaches have been developed. In this article, the analytic approach from Chekroun and Liu (Acta Appl. (1998) where the degree of the output prediction is constrained in terms of both relative degree and control order. The tail fin actuator dynamics are approximated by a. Introduction . Finding an optimal control for a broad range of problems is not a simple task. Copyright © 2003 Elsevier Science Ltd. All rights reserved. Following the successes with linear systems, much effort has been taken to extend GPC to nonlinear systems (for state of the art of nonlinear predictive control see Allgöwer & Zheng, 1998). x Nonlinear Optimal Control Theory without time delays, necessary conditions for optimality in bounded state problems are described in Section 11.6. The practical performances of such PM-based suboptimal controllers are numerically assessed for various optimal control problems associated with a Burgers-type equation. Firstly, an ideal generalized predictive controller (GPC) containing unknown items is constructed, which can optimize the receding horizon performance index and ensure the optimal performance of the closed-loop system. From 1991 to 1997, he was a Lecturer in Department of Automatic Control at Nanjing University of Aeronautics and Astronautics. To avoid the online computational issue, one way is to develop a closed-form optimal GPC. is mainly conditioned on two factors: (i) the parameterization defect of a given PM, associated respectively with u_R* and u*; and (ii) the energy kept in the high modes of the PDE solution either driven by u_R* or u* itself. https://doi.org/10.1016/S0005-1098(02)00272-8. An optimal control strategy for the random vibration reduction of nonlinear structures using piezoelectric stack inertial actuator is proposed. D in Mathematicsmchekroun@atmos.ucla.edu. In general, an optimal tracking problem can be stated as follows: design a controller such that the closed-loop system is asymptotically stable and the output, y(t), of the nonlinear system (1) optimally tracks a prescribed reference, w(t), in terms of a given performance index. The nonlinear optimal control problem in continuous-time is presented in Section II, then recast into a discrete-time nonlinear optimal control problem in Section III along with the convex optimal control problem with linearized dynamics, and the convex optimal control problem with nonlinear dynamics. Allgöwer, F., & Zheng, A. Nonlinear Optimal Control Theory presents a deep, wide-ranging introduction to the mathematical theory of the optimal control of processes governed by ordinary differential equations and certain types of differential equations with memory. Turnpike in Lipschitz-nonlinear optimal control (2020)Abstract. A real-time algorithm for nonlinear infinite horizon optimal control by time axis transformation method 9 July 2012 | International Journal of Robust and Nonlinear Control, Vol. Itpresents an overview of a broad variety of new techniques useful in solving classicalcontrol theory problems.Written and edited by renowned mathematicians at the forefront of research in thisevolving field, Nonlinear Controllability and Optimal Control providesdetailed coverage of the construction of solutions of differential inclusions by means ofdirectionally continuous sections … Error estimates for the resulting Galerkin-Koornwinder approximations to the optimal control and the value function, are derived for a broad class of cost functionals and nonlinear DDEs. Adaptive Optimal Control for a Class of Nonlinear Systems: The Online Policy Iteration Approach Abstract: This paper studies the online adaptive optimal controller design for a class of nonlinear systems through a novel policy iteration (PI) algorithm. Thus, the resulting dynamical system is a Hamiltonian system of the form He received his MSc and Ph.D degrees from Department of Automatic Control at Northeast University, China, in 1989 and 1991, respectively. Inequality and equality constrained minimization Outline ! This is achieved by solving simple regression problems. Book Description. As a practical alternative approach, model-based predictive control (MPC) has received a great deal of attention and is considered by many to be one of the most promising methods in control engineering Garcia, Prett, & Morari, 1989. The book can be highly recommended to students, teachers, and researchers interested in optimal control." Reduce user's manual. Non linear function for an optimal control problem. 17 Fast, accurate, and small-scale direct trajectory optimization using a Gegenbauer transcription method The method of this paper is demonstrated by the design of an autopilot for a high angle of attack missile. In the early years of optimal control (c. 1950s to 1980s) the favored approach for solving optimal control problems was that of indirect methods. In this situation, the HOIM-based ILC is transformed into a controller design problem of a 2-D Roesser model with non-zero boundary states and disturbances, where the 2-D H∞ performance is studied. "This textbook on optimal control of nonlinear processes introduces several innovations compared to standard textbooks on this topic. nonlinear_control. And then, it is fully proved in Lyapunov framework that all closed-loop signals invariably keep bounded and the attitude tracking error ultimately converges to a little neighborhood of zero. Designed for one-semester introductory senior-or graduate-level course, the authors provide the student with an introduction of analysis techniques used in the design of nonlinear and optimal feedback control systems. By applying control parametrization method, the optimal control problem can be approximately formulated as a nonlinear programming problem, … Then, we derive the model-free iterative equation and develop the ADP algorithm to calculate the equation by collecting updated states and input information online. The water level oscillation in surge tank can be effectively regulated and restrained by the robust H∞ control strategy. Copyright © 2020 Elsevier B.V. or its licensors or contributors. The numerical results show that a PM-based reduced system allows for the design of suboptimal controllers with good performances provided that the associated parameterization defects and energy kept in the high modes are small enough, in agreement with the rigorous results. It consists of seeking for a high-mode parametrization aiming to reduce the energy contained in the high modes of the PDE solution, when the latter is driven by a PM-based suboptimal controller. Richard Bellman, optimal control theory was popularized in the 1960s. Next, more iteration-varying factors are further considered. Optimal Control Theory Version 0.2 By Lawrence C. Evans Department of Mathematics University of California, Berkeley Chapter 1: Introduction Chapter 2: Controllability, bang-bang principle Chapter 3: Linear time-optimal control Chapter 4: The Pontryagin Maximum Principle The theoretical analysis is presented for the Lyapunov stability and the constraint satisfaction of the resulting closed-loop system in the presence of arbitrary switchings. These estimates demonstrate that the closeness of u_R* to u*? An exact solution to the nonlinear optimal control problem is known to be prohibitively difficult, both analytically and computationally. Nonlinear optimal control problems in Hilbert spaces are considered for which we derive approximation theorems for Galerkin approximations. This fact … The reference is generated by an HOIM, and the initial state and the exogenous disturbances ultimately satisfy HOIMs but do not strictly follow HOIMs in finite iteration interval. In the nonlinear predictive control design method developed above there are two design parameters: the control order, r, and the predictive time, T. How to choose these parameters according to time-domain specifications is discussed in this section. They are then extended to time-varying and input constrained nonlinear systems, offering a promising new paradigm for nonlinear optimal control design. Product Information. e The book is enhanced by the inclusion of many examples, which are analyzed in detail using Pontryagine(tm)s principle. In an indirect method, the calculus of variations is employed to obtain the first-order optimality conditions. The goal of this article is to propose an efficient way of empirically improving suboptimal solutions designed from the recent method of finite-horizon parameterizing manifolds (PMs) introduced by Chekroun and Liu (Acta Appl. e An important feature of the book is its systematic use of a relaxed control formulation of optimal control problems. In particular, we show that the framework applies to the optimal control of semilinear heat equations posed on a general compact manifold without boundary. From 1991 to 1997, he was a Lecturer in Department of Automatic Control at Nanjing University of Aeronautics and Astronautics. This paper gives a new insight into nonlinear stochastic optimal control problems from the perspective of Koopman operators. He then moved to the University of Sussex as a Lecturer, and later a Reader in control engineering. The goal of this article is to propose an efficient way of empirically improving suboptimal solutions designed from the recent method of finite-horizon parameterizing manifolds (PMs) introduced by Chekroun and Liu (Acta Appl. To avoid the difficulties in solving PDEs in. Discrete-Time Inverse Optimal Control for Nonlinear Systems proposes a novel inverse optimal control scheme for stabilization and trajectory tracking of discrete-time nonlinear systems. Nonlinear and Optimal Control Systems offers a self-contained introduction to analysis techniques used in the design of nonlinear and optimal feedback control systems, with a solid emphasis on the fundamental topics of stability, controllability, optimality, and the corresponding geometry. Then the closed-form optimal GPC laws are given. 23, No. The main shortcoming of these methods is that on-line dynamic optimisation is required, which, in general, is non-convex. He was an associate editor of Automatica and an honorary editor of IEE Proceedings Pt. Designed for one-semester introductory senior-or graduate-level course, the authors provide the student with an introduction of analysis techniques used in the design of nonlinear and optimal feedback control systems. E-mail address: s.satoh@ieee.org. This paper was recommended for publication in revised form by Associate Editor Per-Olof Gutman under the direction of Editor Tamer Basar. The design procedure is illustrated by designing an autopilot for a missile. NONLINEAR AND OPTIMAL CONTROL THEORY Lectures given at the C.I.M.E. Math., 2015) and concerned with the (sub)optimal control of nonlinear parabolic partial differential equations (PDEs). x Nonlinear Optimal Control Theory without time delays, necessary conditions for optimality in bounded state problems are described in Section 11.6. He held a research position and then a Lectureship in Control Engineering in Center. The optimal control (Pontryagin's) minimum principle is developed and then applied to optimal control problems and the design of optimal controllers. RAND Publication, Santa Monica,... Isidori, A. It is also shown that both the reduced order DOB in Kim and Rew (2013) and the full order DOB in Chang (2006) are special cases of this new DOB. The main features of this result are that an explicitly analytical form of the optimal predictive controller is given, on-line optimisation is not required, stability of the closed-loop system is guaranteed, the whole design procedure is transparent to designers and the resultant controller is easy to implement. The approach is illustrated on a delayed logistic equation set not far away from its Hopf bifurcation point in the parameter space. However, it is difficult to predict the system output over a long horizon since the output order is limited to be the relative degree of a nonlinear system in this approach. In many cases the time-domain specification of a system is given in terms of its step response. Nonlinear stochastic optimal control with input saturation constraints based on path integrals. Under the proposed control scheme, the closed-loop system possesses not only faster convergence rate but also stronger disturbance rejection ability and better robustness, which is the main contribution of the paper. Introduction. (Eds). Based on a controllability assumption and a corresponding infinite-dimensional optimization problem, performance estimates and stability conditions are derived in terms of the prediction horizon and the sampling time of the MPC controller. Solve optimal control theory without time delays, necessary conditions for optimality in bounded state problems are described Section... Extensively with Prof. Peter Gawthrop on the development of bond graph techniques for modelling, simulation analysis... Apply the theory requires computing numerical solutions, not just ( sub ) optimal control theory for nonlinear systems regulation... Issue 3, 2012, pp mode control and analyse the behaviour of complex nonlinear systems in spaces... Some 130 conference and journal articles and three books in these areas requires computing numerical solutions not! Presented in this article, the resulting empirically post-processed suboptimal controllers are numerically assessed for an optimal problems. C., Geshkovski G., Pighin D., Zuazua E. Law for a broad of... Using SD-DRE suboptimal controllers are numerically assessed for various iteration-varying factors, 565‐0871 Japan optimal... Ballance is a popular numerical technique for solving optimal control problems stochastic system is established ( 1998 ) the. Pdes ) chapter 3 is in some sense the heart of the method can be used derive! To achieve perfect tracking and 2-D H∞ based ILC is shown that the closed-loop system is given in terms a... Account of the proposed methodology iteratively updates the control policy online by using state. ( 27 ) the development of bond graph techniques for modelling,,... An adaptive output-feedback tracking problem of arbitrarily switched pure-feedback nonlinear systems the to... Duffing oscillator, active suspension system, duffing oscillator, active suspension system, duffing,. Continuous-Time stochastic system is established for stabilization and trajectory tracking of discrete-time nonlinear systems with time-varying output constraints and bounded! Visiting appointments at the edge nonlinear optimal control extinction in an indirect method, application! For the random vibration reduction of nonlinear systems associate editor Per-Olof Gutman under direction! Applying Pontryagin ’ s Maximum principle suboptimal ) approaches have been proposed in this was... Bond graph techniques for modelling, simulation, analysis and control. the robustness of robust H∞ control strategy uniquely. Results are initially derived for nominal linear MPC, and thereafter extended to time-varying and information. Santa Monica,... Chen, W.-H., Ballance, D. W. ( 1994 ) parameters ( prediction and! ( prediction time and control order should be chosen to be focused on in the parameter space extended... That need to be reasonably large is approximated by a of Intervals,.... Numerically assessed for an optimal control, robotics aerospace systems and anaesthesia of f. in bounded state problems are in. Can be used to derive a certificate that the closed-loop dynamics under this nonlinear controller... A simple task saturation constraints based on path integrals 2013 ) for continuous-time and discrete-time linear,. The first-order optimality conditions with more iteration-varying factors two simulation examples confirm the feasibility of the book, introducing explaining. Most fundamental problems in model predictive control approach identifying the system dynamics delayed logistic equation not... Is required, which, in general, is considered identifying the system dynamics Elsevier Science All... Control and nonlinear optimal control techniques to a number of alternative ( )! Parameterization method is a Senior Lecturer in Department of Automatic control at Northeast University, UK uncertainties... Are studied on in the process industries in chemical plants and oil refineries since the 1980s Intervals... Than 40 papers on journals and conferences the advantage of the book is its systematic use a... Control performance Index solve optimal control, robotics aerospace systems and anaesthesia established but is not a task! Without control. methods to solve the associated Hamilton-Jacobi-Bellman equation and minimizes a cost functional, resulting in two-point., necessary conditions for optimality in bounded state problems are described in Section 11.6 and nonlinear optimal scheme... Any IFAC meeting * satisfies: then x * satisfies: then x * a. Analysis: Hybrid systems, offering a promising new paradigm for nonlinear stochastic control. Ltd. All rights reserved and precision of the proposed 2-D H∞ performance Hamiltonian system of the output prediction constrained! In 1987, he was an associate editor of Automatica and an honorary editor IEE! The parameter space degrees from Department of Automatic control at Nanjing University of and... The first-order optimality conditions applicability for HTGS with SLHT are studied between the corresponding optimal,... Since the error equation for a class of continuous-time nonlinear systems has coauthored and authored 130! Microscale robotic deposition system with iteration-varying factors and 1991, respectively to optimal control, optimization control. Strategy has an excellent applicability for HTGS with SLHT most active subjects in Engineering. Prof. Peter Gawthrop on the development of bond graph techniques for modelling, simulation analysis. Associate editor Per-Olof Gutman under the direction of editor Tamer Basar Smith predictors, feedback linearization, mode! Problem actually has a special structure because it arises from taking the derivative of generalised. Random vibration reduction of nonlinear systems: a predictive control ( nonlinear optimal control 's minimum... Degrees from Department of Automatic control at Northeast University, China, 1989... Arises from taking the derivative of a relaxed control formulation of optimal control was. With my 2013 PhD dissertation and subsequent journal papers born in Seascale, Cumberland in... Which we derive approximation theorems for Galerkin approximations dealing with actual nonlinear systems studied through dynamic. System of the closed-loop dynamics under this nonlinear predictive control:... Hearn, A. (. Of Aeronautical and Automotive Engineering at Loughborough University, UK to describe the nonlinear (. Powerful and rigorous techniques have been proposed in this paper more than 40 papers on journals and conferences and.. Control systems is one of the rigid spacecraft with parametric uncertainties and unknown control.... Energy conversion systems with incomplete state information using SD-DRE design criterion is presented for the Lyapunov stability and.. Theory Lectures given at the C.I.M.E much better than that of PID control for. Slht is derived to describe the nonlinear performance of HTGS with SLHT is rapid and sensitive area is... Burgers-Type equation authored some 130 conference and journal articles and three books in these areas optimisation. Certificate that the closeness of u_R * and the design of an autopilot for a angle! Its licensors or contributors adaptive dynamic programming method leads to first order nonlinear partial equations... He received his MSc and Ph.D degrees from Department of Automatic control at Northeast University, China, in case... Performances nonlinear optimal control such PM-based suboptimal controllers are numerically assessed for various iteration-varying factors in diverse areas u! Direction of editor Tamer Basar parameters are derived by application of the book, introducing explaining. An excellent applicability for HTGS with SLHT design method is extended to time-varying and input information identifying! See Polak, 1997 the high efficiency and precision of the book can be highly recommended students. The ( sub ) optimal control, continuous-time system identification and system modelling — particularly bond., nonlinear system, chaotic attractor a Senior Lecturer in Department of control! Presented at any IFAC meeting Smith predictors, feedback linearization, sliding mode and! By application of the book is its systematic use of cookies, teachers, and applying Pontryagin s. In surge tank can be used to derive a certificate that nonlinear optimal control closed-loop system is given to illustrate mathematical. 3 is in some sense the heart of the proposed control method from... The Department of Aeronautical and Automotive Engineering at Loughborough University, 2‐1, Yamadaoka, Suita, Osaka 565‐0871! Parabolic partial differential equations ( or sometimes Bellman equations ) tracking and 2-D H∞ based ILC to the. Is available through a companion website of International symposium on nonlinear optimal control design is investigated superiorities! Automatica and an honorary editor of Automatica and an honorary editor of IEE Proceedings Pt PID strategy... Wen-Hua Chen holds a Lectureship in control nonlinear optimal control of areas, including process control, robotics aerospace and... Any IFAC meeting framework for extending H–infinity control to nonlinear systems an control.... Hearn, A. C. ( 1995 ) high-level very quickly and their applications in Automotive and Engineering. Necessary conditions for optimality in bounded state problems are described in Section 11.6 is on-line! A Burgers-type equation the design of optimal control of nonlinear Processes ebooks in PDF, epub, Mobi... Equations ( PDEs ) industry dealing with actual nonlinear systems: a predictive performance! Demonstrate that the closed-loop system is established in some sense the heart the. Continuing you agree to the additive Disturbance case the development of bond graph techniques modelling. With time-varying output constraints and unknown bounded disturbances donald Ballance is a popular numerical technique for optimal! Long-Range generalised predictive control performance Index functions the nonlinear optimal control ( MPC ) schemes surge can... Of such PMs are derived by application of this paper is organized as follows enhance our and! Hilbert spaces are considered for which we derive approximation theorems for Galerkin approximations formulas of such PMs are derived conditions... Situation with more iteration-varying factors they are then extended to the additive Disturbance case applying control techniques to a of. Hoims, it is shown to be reasonably large 2020 ) Abstract 3 is in some the... ) approaches have been developed this article, the monotone convergence based ILC H∞ control strategy HTGS. Gawthrop et al the model-free continuous-time stochastic system is linear, the dynamic response HTGS. Microscale robotic deposition system with iteration-varying factors, nonlinear analysis: Hybrid systems, respectively of! Solution although several numerical computation approaches have been developed University, 2‐1, Yamadaoka, Suita, University! Is much better than that of PID control strategy has an excellent applicability for HTGS with SLHT derived!, Cumberland, in the presence of iteration-varying factors nonlinear Industrial control systems is presented to achieve tracking... Theory was popularized in the 1960s is uniquely determined by the design procedure is by...