Predictive control of linear uncertain systems

• Main Author: Mu, Huiying
• Published: Imperial College London 2007
• Subjects: 003.5
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.487765

Predictive control is a very useful tool in controlling constrained systems, since the constraints can be satisfied explicitly by the optimisations. Sets, namely, reachable sets, controllable sets, invariant sets, etc, play fundamental roles in designing predictive control strategies for uncertain systems. Meanwhile, in addition to the commonly assumed boundedness of the uncertainty, the explicit use of its stochastic properties can lead to improvement in system response. This thesis is concerned with robust set theories, mainly for reachable sets, with applications to time-optimal control; and the use of stochastic properties of the uncertainty to achieve less conservative controls. In the first part of this thesis, we focus on LTI systems subject to, additional to the usual constraints, a constraint on the control change between sample times. One key ingredient in controlling such constrained systems is the initial control value, which, via analyses and simulations, is shown to be a useful extra degree of freedom. Reachable sets that incorporate this influential initial control value are derived and analyzed, with theoretical as well as computational algorithms developed for both nominal and uncertain systems under different types of feedback policy. Following this, the reachable set is discussed in connection with time-optimal control to obtain desired control laws. In addition, controllable sets, stabilisable sets and invariant sets for such constrained uncertain systems are studied. In the second part, the uncertainties are assumed to have stochastic properties. They are exploited in three different ways: the expected worst-case is used instead of the worst-case to achieve less conservative control even when the uncertainty is relatively large; the stochastic invariant set is proposed to provide alternative methods for approximating disturbance invariant sets; the relaxed set difference is developed to obtain less restrictive controls and/or replacing probabilistic constraint or slack variables.