Control of Systems with Constraints

Motivated by the needs of real engineering systems our objective is to analyse and design linear time invariant systems to achieve high performance such as by pole assignment LQ optimisation and H optimisation and to meet several types of prospeci ed constraints The constraints are imposed on the structure of the controller and on the magnitude of the control input and the system state We choose several topics to re ect di erent practical needs For each topic appropriate advanced techniques from optimisation and control theory are applied to the design of controllers Substantial analysis is carried out to lay a theoretical basis for the computational procedures developed for each of those topics More speci cally as one class of constraint the controller is required to be static output feedback which is appealing for implementation Two important control design objectives quadratic optimal control and pole placement are achieved sub ject to those controller constraints Complexity in the design process resulting from the constraint is addressed by using a gradient ow approach Some algorithms are developed to compute a required controller Attractive convergence properties of these algorithms are obtained As another class of constraint equality constraints on the state space such as a mechanical system subject to holonomic constraints are considered A transfor mation is introduced to convert the original system with constraints into another unconstrained system Then the approach of an H optimal control by static state feedback through the solution of a Riccati equation is applied to achieve the