A sufficient optimality condition for delayed state-linear optimal control problems

We give answer to an open question by proving a sufficient optimality condition for state-linear optimal control problems with time delays in state and control variables. In the proof of our main result, we transform a delayed state-linear optimal control problem to an equivalent non-delayed problem. This allows us to use a well-known theorem that ensures a sufficient optimality condition for non-delayed state-linear optimal control problems. An example is given in order to illustrate the obtained result.Comment: This is a preprint of a paper whose final and definite form is with 'Discrete and Continuous Dynamical Systems -- Series B' (DCDS-B), ISSN 1531-3492, eISSN 1553-524X, available at [http://www.aimsciences.org/journal/1531-3492]. Paper Submitted 31/Dec/2017; Revised 13/April/2018; Accepted 11/Jan/201

Backstepping and Sequential Predictors for Control Systems

We provide new methods in mathematical control theory for two significant classes of control systems with time delays, based on backstepping and sequential prediction. Our bounded backstepping results ensure global asymptotic stability for partially linear systems with an arbitrarily large number of integrators. We also build sequential predictors for time-varying linear systems with time-varying delays in the control, sampling in the control, and time-varying measurement delays. Our bounded backstepping results are novel because of their use of converging-input-converging-state conditions, which make it possible to solve feedback stabilization problems under input delays and under boundedness conditions on the feedback control. Our sequential predictors work is novel in its ability to cover time-varying measurement delays and sampling which were beyond the scope of existing sequential predictor methods for time-varying linear systems, and in the fact that the feedback controls that we obtain from our sequential predictors do not contain any distributed terms

Optimal control of linear systems with large and variable input delays

This paper proposes an optimal control law for linear systems affected by input delays. Specifically we prove that when the delay functions are known it is possible to generate the optimal control for arbitrarily large delay values by using a DDE without distributed terms. The solution can be seen as a chain of predictors whose size depends on the maximum delay