Neural network fitting for input-output manifolds of online control laws in constrained linear systems

Control techniques for systems with constraints on control and state are somewhat attractive, mainly in cases where these constraints represent safety or critical points of operation. An important approach for control of constrained linear systems is based on the concept of set invariance, whose main advantages are the inclusion of constraints in the whole design, the non-conservative nature of the controllers and the ability to cope with noise measurement and disturbance entering in the system. Some disadvantage are a possibly high complexity of the control law for higher order systems or the absence of an analytical, off-line control law in some cases, as, for instance, in the output feedback case. The online computation of the control input at each step is ever possible, but the computational cost involved may turn the solution impracticable in the case of systems with fast dynamics. Neural networks, on the other hand, is an interesting alternative for function approximation, and works well in capturing the characteristics of the input-output manifold of the online control law, starting from a training set generated by simulation of the control system. In this paper, neural networks are applied to substitute in an efficient way the online control computation. A real case based example is used to verify the effectiveness of the proposed neural controller.