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Unformatted text preview: OptimizationBased Control Richard M. Murray Control and Dynamical Systems California Institute of Technology DRAFT v2.1a, January 3, 2010 c circlecopyrt California Institute of Technology All rights reserved. This manuscript is for review purposes only and may not be reproduced, in whole or in part, without written consent from the author. Chapter 3 Receding Horizon Control (with J. E. Hauser and A. Jadbabaie) This set of notes builds on the previous two chapters and explores the use of online optimization as a tool for control of nonlinear control. We begin with a highlevel discussion of optimizationbased control, refining some of the concepts initially in troduced in Chapter 1. We then describe the technique of receding horizon control (RHC), including a proof of stability for a particular form of receding horizon con trol that makes use of a control Lyapunov function as a terminal cost. We conclude the chapter with a detailed design example, in which we can explore some of the computational tradeoffs in optimizationbased control. Prerequisites. Readers should be familiar with the concepts of trajectory generation and optimal control as described in Chapters 1 and ?? . For the proof of stability for the receding horizon controller that we present, familiarity with Lyapunov stability analysis at the level given in AM08, Chapter 4 (Dynamic Behavior) is assumed. The material in this chapter is based on part on joint work with John Hauser and Ali Jadbabaie [MHJ + 03]. 3.1 OptimizationBased Control Optimizationbased control refers to the use of online, optimal trajectory generation as a part of the feedback stabilization of a (typically nonlinear) system. The basic idea is to use a receding horizon control technique: a (optimal) feasible trajectory is computed from the current position to the desired position over a finite time T horizon, used for a short period of time < T , and then recomputed based on the new system state starting at time t + until time t + T + . Development and ap plication of receding horizon control (also called model predictive control, or MPC) originated in process control industries where the processes being controlled are often sufficiently slow to permit its implementation. An overview of the evolution of commercially available MPC technology is given in [QB97] and a survey of the state of stability theory of MPC is given in [MRRS00]. Design approach The basic philosophy that we propose is illustrated in Figure 3.1. We begin with a nonlinear system, including a description of the constraint set. We linearize this system about a representative equilibrium point and perform a linear control design using standard control design tools. Such a design can provide provably robust per formance around the equilibrium point and, more importantly, allows the designer 3.1. OPTIMIZATIONBASED CONTROL 32 Nonlinearities Cost Function Linearized Model Linear Design Linear Controller Linear System Nonlinear System with Constraints...
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This note was uploaded on 01/04/2012 for the course CDS 110b taught by Professor Murray,r during the Fall '08 term at Caltech.
 Fall '08
 Murray,R

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