Optimal dynamic inversion control design for a class of nonlinear distributed parameter systems with continuous and discrete actuators

Abstract

Combining the principles of dynamic inversion and optimisation theory, two stabilising state-feedback control design approaches are presented for a class of nonlinear distributed parameter systems. One approach combines the dynamic inversion with variational optimisation theory and it can be applied when there is a continuous actuator in the spatial domain. This approach has more theoretical significance in the sense that it does not lead to any singularity in the control computation and the convergence of the control action can be proved. The other approach, which can be applied when there are a number of discrete actuators located at distinct places in the spatial domain, combines dynamic inversion with static optimisation theory. This approach has more relevance in practice, since such a scenario appears naturally in many practical problems because of implementation concern. These new techniques can be classified as 'design-then-approximate' techniques, which are in general more elegant than the 'approximate-then-design' techniques. However, unlike the existing design-then-approximate techniques, the new techniques presented here do not demand involved mathematics (like infinite-dimensional operator theory, inertial manifold theory and so on). To demonstrate the potential of the proposed techniques, a real-life temperature control problem for a heat transfer application is solved, first assuming a continuous actuator and then assuming a set of discrete actuators.