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Adaptive dynamic programming is a collective term for a variety of approaches to infinite-horizon optimal control. Common to all approaches is approximation of the infinitehorizon cost function based on dynamic programming philosophy. Typically, they also require knowledge of a dynamical model of the system. In the current work, application of adaptive dynamic programming to a system whose dynamical model is unknown to the controller is addressed. In order to realize the control algorithm, a model of the system dynamics is estimated with a Kalman filter. A stacked control scheme to boost the controller performance is suggested. The functioning of the new approach was verified in simulation and compared to the baseline represented by gradient descent on the running cost.

Sliding‐mode control is a wide‐spread approach to a number of practical problems. The classical stability analyses of sliding‐mode control had to face the difficulty of defining a trajectory of a system whose dynamics are discontinuous in the state variable. Different generalizations of the system trajectory were suggested, such as Filippov solutions. Another generalization is based on the sample‐and‐hold framework, where the system dynamics are in continuous time and the control is changed only at certain discrete times. The current work addresses the sample‐and‐hold stability analysis of sliding‐mode control with special attention to an explicit computation of the required controller sampling time. A computational example is provided.

We provide a computer-assisted approach to ensure that a given continuous or discrete-time polynomial system is (asymptotically) stable. Our framework relies on constructive analysis together with formally certified sums of squares Lyapunov functions. The crucial steps are formalized within of the proof assistant Minlog. We illustrate our approach with various examples issued from the control system literature.