Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userProvably Correct Controller Synthesis of Switched Stochastic Systems with Metric Temporal Logic Specifications: A Case Study on Power Systems
101
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In this paper, we present a provably correct controller synthesis approach for switched stochastic control systems with metric temporal logic (MTL) specifications with provable probabilistic guarantees. We first present the stochastic control bisimulation function for switched stochastic control systems, which bounds the trajectory divergence between the switched stochastic control system and its nominal deterministic control system in a probabilistic fashion. We then develop a method to compute optimal control inputs by solving an optimization problem for the nominal trajectory of the deterministic control system with robustness against initial state variations and stochastic uncertainties. We implement our robust stochastic controller synthesis approach on both a four-bus power system and a nine-bus power system under generation loss disturbances, with MTL specifications expressing requirements for the grid frequency deviations, wind turbine generator rotor speed variations and the power flow constraints at different power lines.
rate research
Read More
In this paper, we present a controller synthesis approach for wind turbine generators (WTG) and energy storage systems with metric temporal logic (MTL) specifications, with provable probabilistic guarantees in the stochastic environment of wind power generation. The MTL specifications are requirements for the grid frequency deviations, WTG rotor speed variations and the power flow constraints at different lines. We present the stochastic control bisimulation function, which bounds the divergence of the trajectories of a switched stochastic control system and the switched nominal control system in a probabilistic fashion.We first design a feedforward controller by solving an optimization problem for the nominal trajectory of the deterministic control system with robustness against initial state variations and stochastic uncertainties. Then we generate a feedback control law from the data of the simulated trajectories. We implement our control method on both a four-bus system and a nine-bus system, and test the effectiveness of the method with a generation loss disturbance. We also test the advantage of the feedback controller over the feedforward controller when unexpected disturbance occurs.
Given a Markov decision process (MDP) and a linear-time ($omega$-regular or LTL) specification, the controller synthesis problem aims to compute the optimal policy that satisfies the specification. More recently, problems that reason over the asymptotic behavior of systems have been proposed through the lens of steady-state planning. This entails finding a control policy for an MDP such that the Markov chain induced by the solution policy satisfies a given set of constraints on its steady-state distribution. This paper studies a generalization of the controller synthesis problem for a linear-time specification under steady-state constraints on the asymptotic behavior. We present an algorithm to find a deterministic policy satisfying $omega$-regular and steady-state constraints by characterizing the solutions as an integer linear program, and experimentally evaluate our approach.
We present a data-driven framework for strategy synthesis for partially-known switched stochastic systems. The properties of the system are specified using linear temporal logic (LTL) over finite traces (LTLf), which is as expressive as LTL and enables interpretations over finite behaviors. The framework first learns the unknown dynamics via Gaussian process regression. Then, it builds a formal abstraction of the switched system in terms of an uncertain Markov model, namely an Interval Markov Decision Process (IMDP), by accounting for both the stochastic behavior of the system and the uncertainty in the learning step. Then, we synthesize a strategy on the resulting IMDP that maximizes the satisfaction probability of the LTLf specification and is robust against all the uncertainties in the abstraction. This strategy is then refined into a switching strategy for the original stochastic system. We show that this strategy is near-optimal and provide a bound on its distance (error) to the optimal strategy. We experimentally validate our framework on various case studies, including both linear and non-linear switched stochastic systems.
This paper studies the robust satisfiability check and online control synthesis problems for uncertain discrete-time systems subject to signal temporal logic (STL) specifications. Different from existing techniques, this work proposes an approach based on STL, reachability analysis, and temporal logic trees. Firstly, a real-time version of STL semantics and a tube-based temporal logic tree are proposed. We show that such a tree can be constructed from every STL formula. Secondly, using the tube-based temporal logic tree, a sufficient condition is obtained for the robust satisfiability check of the uncertain system. When the underlying system is deterministic, a necessary and sufficient condition for satisfiability is obtained. Thirdly, an online control synthesis algorithm is designed. It is shown that when the STL formula is robustly satisfiable and the initial state of the system belongs to the initial root node of the tube-based temporal logic tree, it is guaranteed that the trajectory generated by the controller satisfies the STL formula. The effectiveness of the proposed approach is verified by an automated car overtaking example.
This paper studies the controller synthesis problem for Linear Temporal Logic (LTL) specifications using (constrained) zonotope techniques. To begin with, we implement (constrained) zonotope techniques to partition the state space and further to verify whether the LTL specification can be satisfied. Once the LTL specification can be satisfied, the next step is to design a controller to guarantee the satisfaction of the LTL specification for dynamic systems. Based on the verification of the LTL specification, an abstraction-based control design approach is proposed in this paper: a novel abstraction construction is developed first, then finite local abstract controllers are designed to achieve the LTL specification, and finally the designed abstract controllers are combined and refined as the controller for the original system. The proposed control design strategy is illustrated via a numerical example from autonomous robots.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
