Finite Horizon H8 and Related Control Problems

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.

Contenu

1 Necessary Conditions for Optimality in Problems with Nonstandard Cost Functionals.- 1. Introduction.- 2. Preliminaries.- 3. Necessary Conditions For Optimality.- 4. Cost Functional Of The Form Of A Product.- 5. Certain Generalizations.- References.- 2 Synthesis of Suboptimal H? Controllers over a Finite Horizon.- Abstract.- 1. Introduction.- 2. Finite Horizon Problem.- 3. Computation Of $$\tilde \lambda $$.- 4. A Differential Equation For $$\tilde \lambda $$.- 5. Examples.- 6. A Suboptimal Feedback Controller.- 7. Conclusions.- References.- 3 General Formulae for Suboptimal H? Control over a Finite Horizon.- Abstract.- 1. Introduction.- 2. Problem Formulation.- 3. Full State Feedback Problem.- 4. Output Feedback Controller.- 5. Summary Of Results.- 6. Conclusions.- References.- 4 Finite Horizon H? with Parameter Variations.- Abstract.- 1. Introduction.- 2. Problem Formulation.- 3. Feedback Solutions.- 4. Computation Of Performance.- 5. Performance Variation.- 6. Performance Robustness Problem Solution.- 7. An Example.- 8. Conclusions.- References.- 5 A General Minimization Problem with Application to Performance Robustness in Finite Horizon H?.- Abstract.- 1. Introduction.- 2. Existence Of A Minimizer.- 3. Characterization Of v0 And $$\tilde \lambda $$.- 4. Variation Of The Minimum Value.- 5. Application To Performance Robustness.- 6. Conclusions.- References.- 6 H? Design of the F/A-18A Automatic Carrier Landing System.- Abstract.- 1. Introduction.- 2. H? Controller Design.- 3. Actuator And Engine Dynamics.- 4. Response To Disturbances.- 5. Conclusions.- References.