Optimal linear control systems with input derivative constraints

A very significant result in modern control theory is that, for a linear, finite-dimensional, dynamical system, the state feedback law derived from a quadratic-loss-function minimisation problem is linear. The paper applies the results of this optimal control theory to a class of problems in which the feedback law is realised by a linear dynamical system. The quadratic loss function of interest in this case consists of terms involving time derivatives of the input vector as well as the usual terms involving the input and state vectors. Optimal control problems of this type may arise, for example, when the input force or energy is to be included in the cost terms of the performance index. An advantage of the controllers resulting from the optimisation procedure is that they are dynamic, and thus possess finite bandwidth; accordingly they can be used when there is a limitation to the bandwidth of a communication channel over which feedback signals are transmitted.