A fundamental problem in automatic control is the control of uncertain plants in the presence of input and state or output constraints. An elegant and theoretically most satisfying framework is represented by optimal control policies which, however, rarely gives an analytical feedback solution, and oftentimes builds on numerical solutions (approximations).Therefore, in practice, the problem has seen many ad-hoc solutions, such as override control, anti-windup, as well as modern techniques developed during the last decades usually based on state space models. One of the popular example is Model Predictive Control (MPC) where an optimal control problem is solved at each sampling instant, and the element of the control vector meant for the nearest sampling interval is applied. In spite of the increased computational power of control computers, MPC is at present mainly suitable for low-order, nominally linear systems. The robust version of MPC is conservative and computationally complicated, while the explicit version of MPC that gives an affine state feedback solution involves a very complicated division of the state space into polyhedral cells.In this thesis a novel and computationally cheap solution is presented for linear, time-varying or uncertain, discrete-time systems with polytopic bounded control and state (or output) vectors, with bounded disturbances. The approach is based on the interpolation between a stabilizing, outer controller that respects the control and state constraints, and an inner, more aggressive controller, designed by any method that has a robustly positively invariant set within the constraints. A simple Lyapunov function is used for the proof of closed loop stability.In contrast to MPC, the new interpolation based controller is not necessarily employing an optimization criterion inspired by performance. In its explicit form, the cell partitioning is simpler that the MPC counterpart. For the implicit version, the on-line computational demand can be restricted to the solution of one linear program or quadratic program. Several simulation examples are given, including uncertain linear systems with output feedback and disturbances. Some examples are compared with MPC. The control of a laboratory ball-and-plate system is also demonstrated. It is believed that the new controller might see wide-spread use in industry, including the automotive industry, also for the control of fast, high-order systems with constraints.
