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This work investigates robust monotonic convergent iterative learning control (ILC) for uncertain linear systems in both time and frequency domains, and the ILC algorithm optimizing the convergence speed in terms of $l_{2}$ norm of error signals is derived. Firstly, it is shown that the robust monotonic convergence of the ILC system can be established equivalently by the positive definiteness of a matrix polynomial over some set. Then, a necessary and sufficient condition in the form of sum of squares (SOS) for the positive definiteness is proposed, which is amendable to the feasibility of linear matrix inequalities (LMIs). Based on such a condition, the optimal ILC algorithm that maximizes the convergence speed is obtained by solving a set of convex optimization problems. Moreover, the order of the learning function can be chosen arbitrarily so that the designers have the flexibility to decide the complexity of the learning algorithm.
A robust Learning Model Predictive Controller (LMPC) for uncertain systems performing iterative tasks is presented. At each iteration of the control task the closed-loop state, input and cost are stored and used in the controller design. This paper f
We present a convex optimization to reduce the impact of sensor falsification attacks in linear time invariant systems controlled by observer-based feedback. We accomplish this by finding optimal observer and controller gain matrices that minimize th
In the interaction between control and mathematics, mathematical tools are fundamental for all the control methods, but it is unclear how control impacts mathematics. This is the first part of our paper that attempts to give an answer with focus on s
In this paper, we consider the application of optimal periodic control sequences to switched dynamical systems. The control sequence is obtained using a finite-horizon optimal method based on dynamic programming. We then consider Euler approximate so
Accounting for more than 40% of global energy consumption, residential and commercial buildings will be key players in any future green energy systems. To fully exploit their potential while ensuring occupant comfort, a robust control scheme is requi