Mpc and constrained systems a general methodology model predictive control is a form of control in which the current control action is obtained by solving, at each sampling instant, a finite horizon openloop optimal control problem, using the current state of the plant as the initial state. Hybrid control addresses the problem of integrating the minimization and maximization for decision making in this context. Optimal control for nonlinear hybrid systems via convex relaxations pengcheng zhao, shankar mohan, and ram vasudevan abstract this paper considers the optimal control for hybrid systems whose trajectories transition between distinct sub systems when statedependent constraints are satis. A descent algorithm for the optimal control of constrained nonlinear switched dynamical systems. Paiva 1 1 department of electrical and computer engineering university of porto, faculty of engineering rua dr.
The theory of explicit mpc, where the nonlinear optimal feedback controller can be calculated efficiently, is presented in the context of linear systems with linear constraints, switched linear systems, and, more generally, linear hybrid systems. First, we give basic theoretical results on the structure of the optimal statefeedback solution and of the value function. From the solution of the discretized problem, a value function that preserves the lower bound property can be constructed. Robust control of hybrid systems can be achieved using the iss technique, see 17. Time optimal control and robust time optimal control of constrained linear, dis cretetime systems may be achieved using, respectively, the controllability and robust controllability sets described above 4,29. A new algorithm for constrained finite time optimal. Convex constrained optimal control problem minimize j. The most important algorithms feature in an accompanying free online matlab toolbox, which allows easy access to sample solutions. For discretetime linear hybrid systems, we have described an offline procedure to synthesize optimal control laws based on the minimization of quadratic and linear performance indices subject to linear constraints on inputs and states. Borrelli and others published constrained optimal control of linear and hybrid systems find, read and cite all the. Optimal persistent disturbance attenuation control for.
Constrained finite time optimal control of pwa systems algebraic manipulation linear performance index p1,1 constraints receding horizon control mixed integer linear program milp plant output y plant state x apply u 0 optimization problem milp obtain ux receding horizon control online optimization. Consistent approximations for the optimal control of. This paper considers an optimal control problem for a class of controlled hybrid dynamical systems hdss with prescribed switchings. Predictive control for linear and hybrid systems, f. First, we show that the closed form of the state feedback solution to finite time optimal control based on quadratic or linear norms performance criteria is a timevarying piecewise affine state feedback control. Optimal covariance control for stochastic linear systems. Second, we describe how the statefeedback optimal control law can be. Model predictive control for linear and hybrid systems. Christophersen, and manfred morari, fellow, ieee abstractwe consider the constrained. First, we show that the closed form of the state feedback solution to finite time optimal control based on quadratic or linear norms performance criteria is a timevarying piecewise affine state feedback control law.
Traction control tc antilock braking system abs electronic stabilty program esp roll pitch fx f fz y nonlinear piecewise linear and constrained system maximum tire slip acceleration zone maximum cornering maximum braking lateral force longitudinal steer angle force active front steering afs systems active suspension systems active. The online implementation ofthe control law requires simply the evalu ation ofthe pwa controller in the ordered region sense note that the order the solution is stored is important. Boost converters proximate constrained timeoptimal. An approximation of the optimal feedback control law is given and tried on some examples. It is assumed that u q is a polytope assigned to each mode q. Based on the use of the calculus of variations, necessary. On optimal control of stochastic linear hybrid systems.
Optimal robust control for constrained nonlinear hybrid systems with. Consistent approximations for the optimal control of constrained switched systems ramanaryan vasudevan, humberto gonzalez, ruzena bajcsy, and s. Predictive control assets cambridge university press. The book focuses on two classes of discretetime dynamical systems, namely constrained linear systems and linear hybrid systems. Model predictive control for linear and hybrid systems robust.
Dynamic programming for constrained optimal control of discrete. Read predictive control for linear and hybrid systems online, read in mobile or kindle. Shankar sastry august 21, 2012 abstract though switched dynamical systems have shown great utility in modeling a variety of physical phe. The focus is on constrained linear systems and constrained linear hybrid systems. Hybrid optimal control under mode switching constraints. We consider a class of first order linear hybrid systems with saturation. Neuralnetworkbased constrained optimal control scheme for. Abstract in this paper we present a modication of the algorithm described in 1, 2 for computing the solution to the constrained nite time optimal control problem for discrete time linear hybrid. Optimal control of a class of linear hybrid systems with. We developed the declarative language hysdel hybrid system description language which fully automatizes the construction of mld and piecewise affine pwa forms from a high level description of the hybrid system. Technical report ucbeecs20109, eecs department, university of california, berkeley, jan 2010.
Constrained timeoptimal control of linear parameter. Control of constrained dynamic systems sciencedirect. By leveraging partial knowledge of system dynamics and constraint enforcing multiobjective loss functions, the method can learn from small and static datasets, handle timevarying state and input constraints and enforce the. A survey of the maximum principles for optimal control. Optimal estimation and filtering methods are included, and optimal fault estimation, safetycritical, faulttolerant and. In the second part of the book we focus on linear systems with polyhedral constraints on inputs and states. Though the determination of a numerical solution for the general nonconvex optimal control problem for hybrid systems has been pursued relentlessly to date, it has proven difficult, since it demands nominal mode scheduling.
Model predictive control for linear and hybrid systems robust constrained optimal. Download pdf predictive control for linear and hybrid. Borelli and others published constrained optimal control of linear and hybrid systems find, read and cite all the research you need on researchgate. Abstractthis paper studies optimal timebounded control in a simple subclass of linear hybrid systems, which consists of one continuous variable and global constraints. Optimal control for nonlinear hybrid systems via convex. Optimal hybrid control for switched ane systems under safety and liveness constraints. Optimal covariance control for stochastic linear systems subject to integral quadratic state constraints efstathios bakolas. One of the oldest problems in the study of dynamical systems is the calculation of an optimal control. Oct 01, 2005 read dynamic programming for constrained optimal control of discretetime linear hybrid systems, automatica on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. This paper presents a novel datadriven method for learning deep constrained continuous control policies and dynamical models of linear systems. First we give basic theoretical results on the structure of the optimal state feedback solution and of the value function. Constrained optimal control of linear and hybrid systems spin springers internal project number, if known monograph february 20, 2003 springer berlin heidelberg newyork hongkong london milan paris tokyo. Optimal robust control for constrained nonlinear hybrid systems with application to bipedal locomotion quan nguyen and koushil sreenath abstractrecent work on control lyapunov functions and control barrier functions has enabled addressing stability of nonlinear and underactuated hybrid systems while simultane. Hybrid optimal control under mode switching constraints with.
Hybrid dynamical system modeling of converters, which directly takes into account the switching nature of the dcdc converters, promises better transient response and large signal stability 49. Minmax control of constrained uncertain discretetime. The optimal adaptive control of systems is of interest and largescale systems, distributed systems and timedelay systems. We focus on hybrid systems with linear dynamics and a xed time horizon.
The procedure is based on a combination of dynamic programming and multiparametric quadratic programming. Our approach uses chance constrained programming 37 to nd a lowcost control strategy while satisfying probabilistic safety constraints. A hybrid optimization method for constrained optimal. Predictive control for linear and hybrid systems by. Optimal control for constrained hybrid system computational libraries and applications l. Predictive control for linear and hybrid systems is an ideal reference for graduate, postgraduate and advanced control practitioners interested in theory and or implementation aspects of predictive control. A hybrid optimization method for constrained optimal control problem akbar banitalebi, mohd ismail abd aziz, rohanin ahmad department of mathematical sciences, faculty of science, universiti teknologi malaysia, 810 skudai, johor, malaysia abstract a new hybrid algorithm by integrating a nested partitions np method with successive quadratic. In this paper we study the solution to optimal control problems for constrained discretetime linear hybrid systems based on quadratic or linear performance criteria. This type of problem has been addressed in the context of constrained optimal control, and, in particular, in the context of robust receding horizon control rhc and robust model predictive control mpc, see e. All the main results presented in the book are contributed originally by the author and his collaborators.
Constrained optimal control of linear and hybrid systems francesco borrelli many practical control problems are dominated by characteristics such as state, input and operational constraints, switches between different operating regimes, and the interaction of continuoustime and discrete event systems. Constrained optimal control of linear and hybrid systems springer. Constrained optimal control of discretetime linear hybrid. Some results on the structure and computation of the optimal control laws are presented. Consider a mpc algorithm for a linear plan with constraints.
The control parameterization enhancing transform for constrained optimal control problems volume 40 issue 3 k. Whilst we have been able to establish some important properties for these algorithms for example, conditions for asymptotic stability, the algorithms remain relatively complex. Pdf predictive control for linear and hybrid systems. Statebased mpc conceptual idea of mpc optimal control synthesis example lateral control of a car stability lecture 15. A new algorithm for constrained finite time optimal control. Predictive control for linear and hybrid systems by francesco borrelli.
A system that belongs to this class can operate in several modes or phases. The proposed approach is based on standard results from the theory of lagrangian duality as in 12. This paper investigates the optimal control problem of a particular class of hybrid dynamical systems with controlled switching. Calculus of variations and nonlinear optimization based.
It also covers optimal control of hybrid systems, switching systems, repetitive and periodic control. Constrained optimal control of linear and hybrid systems. Constrained optimal control of hybrid systems with a linear performance index mato baotic. His research interests include constrained optimal control, model predictive control.
Neuralnetworkbased constrained optimal control scheme. Constrained optimal control of hybrid systems with a linear performance index. The optimal control problem can be viewed as a deterministic zerosum dynamic game between two players. Constrained optimal hybrid control of a flow shop system 2271 last three decades. Constrained timeoptimal control of linear parametervarying. Constrained optimal control of linear and hybrid systems published in. Predictive control for linear and hybrid systems in. Raischzxabstract in this contribution, we propose a twolevel hierarchical control strategy to solve the problem of minimising a cost function for a switched ane system under safety and live. Optimal robust control for constrained nonlinear hybrid. Hence, robust control of constrained linear where is such that is real and diagonal.
Constrained optimal control for hybrid systems springerlink. Download predictive control for linear and hybrid systems ebook free in pdf and epub format. Vickson, in 5, considered the singlemachine sequencing problem with the objective of minimizing a total schedule cost consisting of service costs, assumed to be decreasing linear functions of processing times, and weighted completiontime. The purpose of this study is to realize the adaptive method of linear programming for constructing the optimal open loop control of a class of hybrid system.
A useful outcome of considering the switching nature of dcdc converters is the time optimal control toc of the converters 1012. The effectiveness of the techniques is illustrated on a wide range of practical applications. Control with constraints of a class of hybrid systems. Predictive control for linear and hybrid systems ieee xplore. Each state has a continuous cost attached to it, which is linear in the sojourn time, while a discrete cost. International journal of control 75, 1617 2002, 14061426. By leveraging partial knowledge of system dynamics and constraint enforcing multiobjective loss functions, the method can learn from small and static datasets, handle timevarying state and input constraints and enforce the stability properties of. Mato baotic, francesco borrelli, alberto bemporad, and manfred morari abstract. He is author of the book constrained optimal control of linear and hybrid systems published by springer verlag.
Optimal control of switching surfaces in hybrid dynamical. Francesco borrelli many practical control problems are dominated by characteristics such as state, input and operational constraints, alternations between different operating regimes, and the interaction of. Though this class of systems is useful while modeling a. Given a prespecified sequence of active subsystems, the objective is to seek both the continuous control input and the discrete switching instants that minimize a performance index over a finite time horizon. Francesco borrelli constrained optimal control of linear and hybrid systems spin springers internal project number, if known monograph february 20, 2003. Optimal control of switched systems via non linear optimization based on direct differentiations of value functions. Constrained optimal control problems with linear and quadratic objective functions are dened. Optimal hybrid control for switched ane systems under. For linear and hybrid systems, constrained time optimal control was shown to be a low complexity alternative to the explicit solution of the constrained finitetime opt imal control problem. The synthesized controller is a discretetime controller. Vehicle dynamics control a driver aid for atypical road conditions, such as slippery, windy an bumpy roads yaw l a t e r a l f o r c e tire forces longitudinal force slip target traction control tc antilock braking system abs electronic stabilty program esp roll pitch fx f fz y nonlinear piecewise linear and constrained system maximum.
The early optimal control of mission critical systems becomes highly crucial for preventing failure of equipment. The applicability of the theory is demonstrated through two experimental case studies. Borrelli, constrained optimal control of linear and hybrid systems series title lecture notes in control and information sciences, usa, ny, new york. He is the winner of the innovation prize 2004 from the electroswiss foundation. Overview optimal control applications and methods wiley.
A descent algorithm for the optimal control of constrained. For hybrid systems we study constrained optimal controllers which are able to stabilize hybrid systems on desired reference. Model predictive control for linear and hybrid systems robust constrained optimal control francesco borrelli department of mechanical engineering. This type of problem has been addressed in the context of constrained optimal control, and, in particular, in the context of robust receding horizon control rhc and robust. Dynamic programming for constrained optimal control of. Predictive control for linear and hybrid systems by francesco. Currently he is an assistant professor at the universita del sannio, benevento, italy. The control parameterization enhancing transform for. In this chapter we study the solution to optimal control problems for discrete time linear hybrid systems. In this paper we study the solution to optimal control problems for constrained discretetime linear hybrid systems based on quadratic or linear performance. Minmax control of constrained uncertain a simple function. By using ekelands variational principle and a matrix cost functional, a minimum principle for hdss is derived, which provides a necessary condition of the aforementioned problem. Dynamicprogrammingforconstrainedoptimalcontrolofdiscrete. Rm is the control input, and the disturbance input dt is contained in d.
637 329 1235 1064 564 799 645 1664 854 1089 1499 595 558 1574 657 1573 1375 205 342 1346 1478 592 243 1400 1133 1186 379 861 774 144 825 891 1655 128 705 930 858 1025 134 1329 888 562 416 1147 430 959