Control Theory
Current research in Control Theory at Bath is focused on (a) infinite-dimensional systems and (b) differential inclusions each with application to issues of modelling, robustness and adaptive control of uncertain dynamical systems. Current research includes the programs listed below on asymptotic behaviour of functions, universal adaptive controllers, error regulation, stability of feedback systems and nonsmooth analysis. The members of staff involved are Professor H. Logemann and Professor E.P. Ryan.
- An investigation of asymptotic behaviour of integrable functions in the development of invariance principles for dynamical systems modelled by differential equations, differential inclusions and abstract semi-flows. This work is aimed at refining existing results pertaining to ordinary differential equations/inclusions (such as LaSalle's invariance principle, and the Byrnes-Martin integral-invariance principle) and developing infinite-dimensional analogues of these applicable to semi-flows on metric spaces, and classes of non-autonomous processes encompassing semi-linear evolution systems.
- Application of such invariance principles in analysis and design of universal adaptive controllers for classes of uncertain systems. By universal is meant the following: let P be a set of systems to be controlled (usually each element of P is given by a controlled and observed differential equation (ordinary, functional, partial or an abstract evolution equation), integral equation, integro-differential equation or differential inclusion; a single (adaptive) control strategy is deemed universal if it guarantees that every member of P exhibits some prescribed dynamic behaviour (typically, attractivity of an equilibrium or asymptotic tracking of some reference signal). Unlike most classical control strategies, universal controllers are not based on system identification or parameter estimation algorithms or injection or probing signals: the objective is not to identify, but simply to control the unknown system.
- A study of adaptive integral control addressing the problem (widely encountered in engineering practice) of designing an adaptive controller for an imprecisely known, but stable, process in order to achieve asymptotic error regulation and disturbance rejection for constant reference (set-point) and disturbance signals, with particular emphasis on actuator nonlinearities of saturation, deadzone and hysteresis type.
- The effect of delays in the feedback loop on stability of feedback systems; conditions for robustness and nonrobustness with respect to small delays.
- Nonsmooth analysis, set-valued maps and differential inclusions with applications to modelling and stabilisation - by non-smooth feedback - of (uncertain) nonlinear systems.
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