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Über dieses Buch

HIS book presents a generalized state-space theory for the analysis T and synthesis of finite horizon suboptimal Hoo controllers. We de­ rive expressions for a suboptimal controller in a general setting and propose an approximate solution to the Hoo performance robustness problem. The material in the book is taken from a collection of research papers written by the author. The book is organized as follows. Chapter 1 treats nonlinear optimal control problems in which the cost functional is of the form of a quotient or a product of powers of definite integrals. The problems considered in Chap­ ter 1 are very general, and the results are useful for the computation of the actual performance of an Hoo suboptimal controller. Such an application is given in Chapters 4 and 5. Chapter 2 gives a criterion for the evaluation of the infimal Hoc norm in the finite horizon case. Also, a differential equation is derived for the achievable performance as the final time is varied. A general suboptimal control problem is then posed, and an expression for a subopti­ mal Hoo state feedback controller is derived. Chapter 3 develops expressions for a suboptimal Hoo output feedback controller in a very general case via the solution of two dynamic Riccati equations. Assuming the adequacy of linear expressions, Chapter 4 gives an iterative procedure for the synthesis of a suboptimal Hoo controller that yields the required performance even under parameter variations.

Inhaltsverzeichnis

Frontmatter

Chapter I. Necessary Conditions for Optimality in Problems with Nonstandard Cost Functionals

Abstract
Usual formulation of optimal control problems involves the minimization of a cost functional which is of the form of a definite integral. In this chapter we develop necessary conditions for an optimal control in the case of problems in which the cost functional is either a quotient or a product of definite integrals. We call such functionals nonstandard, and these naturally arise in Chapters 2,4, and 5 during the computation of the performance of a suboptimal H∞ controller. In Chapters 2,4, and 5 a criterion for the evaluation of the cost functional will be presented in the specialized case of linear systems and quadratic integrands. Preliminary results for problems having a fixed final time and free terminal state are in [1]. Related results can also be found in [2,3]. In this monograph, we consider only fixed final time problems. Problems in which the final time is free are treated in [4]. In Section 5, we discuss the relation of our results to those in [2,3].
M. Bala Subrahmanyam

Chapter 2. Synthesis of Suboptimal H ∞ Controllers over a Finite Horizon

Abstract
In this chapter a finite horizon H optimal control problem is posed and solved. A criterion which is useful for the evaluation of the infimal H norm in the finite horizon case is given. Also, a differential equation is derived for the measure of performance in terms of the final time. A general suboptimal control problem is then posed, and an expression for a suboptimal controller is derived solving the saddle point conditions. An expression for a feedback controller can be derived by solving a dynamic Riccati equation. Also, a criterion that yields the actual performance of the suboptimal controller is given. In the time-invariant case, the finite horizon controller converges to a static controller as the final time becomes large. Examples are given to illustrate the usefulness of the theory.
M. Bala Subrahmanyam

Chapter 3. General Formulae for Suboptimal H ∞ Control over a Finite Horizon

Abstract
In this chapter a general suboptimal control problem is posed, and an expression for a suboptimal controller is derived solving the saddle point conditions. Based on this, a formula for a state feedback suboptimal controller can be derived by solving a dynamic Riccati equation. Then an expression for a suboptimal output feedback controller is developed in a general case via the solution of two dynamic Riccati equations.
M. Bala Subrahmanyam

Chapter 4. Finite Horizon H ∞ with Parameter Variations

Abstract
In this chapter we consider the finite horizon H performance robustness problem with parameter variations. Assuming the adequacy of linear expressions for performance variation, an iterative procedure is given to synthesize a suboptimal H controller, which yields the required performance even under parameter variations. As a by-product, an expression for the variation of performance due to parameter variations is given for this specific controller by making use of variational theory. An example which illustrates the methodology is worked out under parameter uncertainties.
M. Bala Subrahmanyam

Chapter 5. A General Minimization Problem with Application to Performance Robustness in Finite Horizon H ∞

Abstract
In this chapter we treat a general minimization problem on a finite horizon in which the cost functional is a quotient of two definite integrals. An existence theorem is given for the minimization of the cost functional, and necessary conditions that need to be satisfied by the minimizer are stated. Also, a condition is given for the evaluation of the minimum value of the cost functional. The results are shown to have application to the finite horizon H performance robustness problem. An expression for the variation of the performance in terms of variations in the system matrices is developed.
M. Bala Subrahmanyam

Chapter 6. H ∞ Design of the F/A-18A Automatic Carrier Landing System

Abstract
In this chapter a design of the F/A-18A Automatic Carrier Landing System is accomplished using finite horizon H techniques. If the final time is sufficiently large, the dynamic Riccati equations involved in the design of the suboptimal output feedback controller give rise to constant solutions. Only longitudinal equations of motion are considered, and thrust is incorporated as a control variable. The object of the design is to maintain a constant flight path angle under worst-case conditions of vertical gust and sensor noise during carrier landing. The design yields satisfactory response for vertical rate command as well.
M. Bala Subrahmanyam

Backmatter

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