On Inf-Convolution-Based Robust Practical Stabilization Under Computational Uncertainty

Abstract

This work is concerned with practical stabilization of nonlinear systems by means of inf-convolution-based sample-and-hold control. It is a fairly general stabilization technique based on a generic non-smooth control Lyapunov function (CLF) and robust to actuator uncertainty, measurement noise, etc. The stabilization technique itself involves computation of descent directions of the CLF. It turns out that non-exact realization of this computation leads not just to a quantitative, but also qualitative obstruction in the sense that the result of the computation might fail to be a descent direction altogether and there is also no straightforward way to relate it to a descent direction. Disturbance, primarily measurement noise, complicate the described issue even more. This work suggests a modified inf-convolution-based control that is robust w. r. t. system and measurement noise, as well as computational uncertainty. The assumptions on the CLF are mild, as, e. g., any piece-wise smooth function, which often results from a numerical LF/CLF construction, satisfies them. A computational study with a three-wheel robot with dynamical steering and throttle under various tolerances w. r. t. computational uncertainty demonstrates the relevance of the addressed issue and the necessity of modifying the used stabilization technique. Similar analyses may be extended to other methods which involve optimization, such as Dini aiming or steepest descent.

A framework for online, stabilizing reinforcement learning

“…The work [46] was enabled by forged via the techniques of sample-and-hold stabilization analyses [53]- [55], which was recently extended to the case of stochastic systems [30], [31].…”

“…The goal here is to extend (6) in a way that does not require a direct use of the Lyapunov function, only a stabilizing policy in case of emergency. We present the core of the idea while omitting full details that can be elaborated following the proof techniques of our previous works [30], [31], [46], [54], [55].…”

On stochastic stabilization of sampled systems

“…All these methods require performing optimization at each time step. In fact, a generalization of Theorem 1 for systems of the kind (sys-aug) applies also in the case when the said optimization is non-exact [24], [25]. A final comment should be made about the generator A.…”

“…Whereas the system and actuator uncertainties are relatively easy to address, the major problem is measurement noise [2]. Still, the method of inf-convolutions described above can be shown robust in this regard [25]. Merging this with Theorem 2 could achieve the desired robustness, but it is left for future work due to the scope limitation.…”

Enhancement of Stability on Dc Microgrid Using Dual Seires Virtual Impedance Based Fuzzy Controller Under Variation of Constant Power Load

“…To deal with the nonlinearity, others have invented various types of Lyapunov functions [31]. For example, to prove the local stability of a given equilibrium in a possible function based on the Brayton-Moser method [32] is used.…”