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This paper studies finite-time stability and instability theorems in probability sense for stochastic nonlinear systems. Firstly, a new sufficient condition is proposed to guarantee that the considered system has a global solution.…
We consider the problem of formally verifying almost-sure (a.s.) asymptotic stability in discrete-time nonlinear stochastic control systems. While verifying stability in deterministic control systems is extensively studied in the…
This paper addresses the stability problem for discrete-time switched systems under autonomous switching. Each mode of the switched system is modeled as a Linear Parameter Varying (LPV) system, the time-varying parameters can vary…
Stochastic dynamical systems are fundamental in state estimation, system identification and control. System models are often provided in continuous time, while a major part of the applied theory is developed for discrete-time systems.…
We present a true-dynamics-agnostic, statistically rigorous framework for establishing exponential stability and safety guarantees of closed-loop, data-driven nonlinear control. Central to our approach is the novel concept of conformal…
We address the stability problem for linear switching systems with mode-dependent restrictions on the switching intervals. Their lengths can be bounded as from below (the guaranteed dwell-time) as from above. The upper bounds make this…
When designing optimal controllers for any system, it is often the case that the true state of the system is unknown to the controller, for example due to noisy measurements or partially observable states. Incomplete state information must…
Control Lyapunov function is a central tool in stabilization. It generalizes an abstract energy function -- a Lyapunov function -- to the case of controlled systems. It is a known fact that most control Lyapunov functions are non-smooth --…
In many real-world reinforcement learning (RL) problems, besides optimizing the main objective function, an agent must concurrently avoid violating a number of constraints. In particular, besides optimizing performance it is crucial to…
Design and analysis of stabilizing controllers with safety guarantees for nonlinear systems have received considerable attention in recent years. Control Lyapunov-barrier functions (CLBFs) provide a powerful framework for simultaneously…
Barrier Lyapunov functions are suitable for learning control designs, due to their feature of finite duration tracking. This paper presents fractional barrier Lyapunov functions, provided and compared with the conventional ones in the…
Inspired by the widespread concept of Lyapunov-Krasovskii functionals of complete type, this article proposes an alternative class of functionals, termed Lyapunov-Krasovskii functionals of robust type. Their construction aims at improving…
In this article we introduce new possibilities of bounding the stability constants that play a vital role in the reduced basis method. By bounding stability constants over a neighborhood we make it possible to guarantee stability at more…
Temporal logics provide a formalism for expressing complex system specifications. A large body of literature has addressed the verification and the control synthesis problem for deterministic systems under such specifications. For…
In many human-in-the-loop robotic applications such as robot-assisted surgery and remote teleoperation, predicting the intended motion of the human operator may be useful for successful implementation of shared control, guidance virtual…
In this work, we propose a methodology for the expression of necessary and sufficient Lyapunov-like conditions for the existence of stabilizing feedback laws. The methodology is an extension of the well-known Control Lyapunov Function (CLF)…
Controllers for dynamical systems that operate in safety-critical settings must account for stochastic disturbances. Such disturbances are often modeled as process noise in a dynamical system, and common assumptions are that the underlying…
We present a novel method of optimal robust control through quadratic programs that offers tracking stability while subject to input and state-based constraints as well as safety-critical constraints for nonlinear dynamical robotic systems…
Reach-avoid problems involve driving a system to a set of desirable configurations while keeping it away from undesirable ones. Providing mathematical guarantees for such scenarios is challenging but have numerous potential practical…
Stability margins for linear time-varying (LTV) and switched-linear systems are traditionally computed via quadratic Lyapunov functions, and these functions certify the stability of the system under study. In this work, we show how the more…