For a dynamical system, it is known that the existence of a Lyapunov density implies almost global stability of an equilibrium. It is then natural to ask whether the existence of multiple Lyapunov densities for a nonlinear switched system implies almost global stability, in the same way as the existence of multiple Lyapunov functions implies global stability for nonlinear switched systems. In this work, the answer to this question is shown to be affirmative as long as switchings satisfy a dwell time constraint with an arbitrarily small dwell time. Specifically, as the main result, we show that a nonlinear switched system with a minimum dwell time is almost globally stable if there exist multiple Lyapunov densities which satisfy some compatibility conditions depending on the value of the minimum dwell time. This result can also be used to obtain a minimum dwell time estimate to ensure almost global stability of a nonlinear switched systems. In particular, the existence of a common Lyapunov density implies almost global stability for any arbitrary small minimum dwell time.

In this paper, we address the chance-constrained safe Reinforcement Learning (RL) problem using the function approximators based on Stochastic Model Predictive Control (SMPC) and Distributionally Robust Model Predictive Control (DRMPC). We use Conditional Value at Risk (CVaR) to measure the probability of constraint violation and safety. In order to provide a safe policy by construction, we first propose using parameterized nonlinear DRMPC at each time step. DRMPC optimizes a finite-horizon cost function subject to the worst-case constraint violation in an ambiguity set. We use a statistical ball around the empirical distribution with radius measured by the Wasserstein metric as the ambiguity set. Unlike the sample average approximation SMPC, DRMPC provides a probabilistic guarantee of the out of sample risk and requires lower samples from the disturbance. Then the Q-learning method is used to optimize the parameters in the DRMPC to achieve the best closed-loop performance. Wheeled Mobile Robot (WMR) path planning with obstacle avoidance will be considered to illustrate the efficiency of the proposed method.

We develop a method for determining whether a stochastic system is safe, i.e., whether its trajectories reach unsafe states. Specifically, we define and solve a probabilistic safety problem for Markov processes. Based on the knowledge of the extended generator, we are able to develop an evolution equation, as a system of integral equations, describing the connection between unsafe and initial states. Subsequently, using the moment method, we approximate the infinite-dimensional optimisation problem searching for the largest set of safe states by a finite dimensional polynomial optimisation problem. In particular, we address the above safety problem to a special class of stochastic hybrid processes, namely piecewise-deterministic Markov processes. These are characterized by deterministic dynamics and stochastic jumps, where both the time and the destination of the jumps are stochastic. In addition, the jumps can be both spontaneous (in the style of a Poisson process) or forced (governed by guards). In this case, the extended generator of this process and its corresponding martingale problem turn out to be defined on a rather restricted domain. To circumvent this

This paper presents a systematic approach to design gain-scheduled predictive controllers for wind turbines. The predictive control law is based on Laguerre functions to parameterize control signals and a parameter-dependent cost function that is analytically determined from turbine data. These properties facilitate the design of speed controllers by placement of the closed-loop poles (when constraints are not active) and systematic adaptation towards changes in the operating point. Vibration control of undamped modes is achieved by imposing a certain degree of stability to the closed-loop system. The approach can be utilized to the design of new controllers and to represent existing gain-scheduled controllers as predictive controllers. The numerical example and simulations illustrate the design of a speed controller augmented with active damping of the tower fore-aft displacement.

The smart water infrastructures laboratory is a research facility at Aalborg University, Denmark. The laboratory enables experimental research in control and management of water infrastructures in a realistic environment. The laboratory is designed as a modular system that can be configured to adapt the test-bed to the desired network. The water infrastructures recreated in this laboratory are district heating, drinking water supply, and waste water collection systems. This paper focuses on the first two types of infrastructure. In the scaled-down network the researchers can reproduce different scenarios that affect its management and validate new control strategies. This paper presents four study-cases where the laboratory is configured to represent specific water distribution and waste collection networks allowing the researcher to validate new management solutions in a safe environment. Thus, without the risk of affecting the consumers in a real network. The outcome of this research facilitates the sustainable deployment of new technology in real infrastructures.

In this letter, we study the so-called $\mathbf {p}$ -safety of a Markov chain. We say that a state is $\mathbf {p}$ -safe in a state space $S$ with respect to an unsafe set $U$ if the process stays in the state space and hits the set $U$ with the probability less than $\mathbf {p}$ . We show several ways of computing $\mathbf {p}$ -safety: by means the Dirichlet problem, the evolution equation, the barrier certificates, and the Martin kernel. The set of barrier certificates forms a cone. We show how to generate barrier certificates from the set of extreme points of a cone base.