Provably Correct Controller Synthesis of Switched Stochastic Systems
with Metric Temporal Logic Specifications: A Case Study on Power Systems
- URL: http://arxiv.org/abs/2103.14264v1
- Date: Fri, 26 Mar 2021 04:50:29 GMT
- Title: Provably Correct Controller Synthesis of Switched Stochastic Systems
with Metric Temporal Logic Specifications: A Case Study on Power Systems
- Authors: Zhe Xu and Yichen Zhang
- Abstract summary: We present a provably correct controller synthesis approach for switched control systems with metric logic (MTL) specifications with provable probabilistic guarantees.
We first present the control bisimulation function for switched control systems, which bounds trajectory divergence between the switched control system and its nominal deterministic control system.
We then develop a method to compute optimal control inputs by solving an optimization problem for the nominal trajectory of the deterministic control system.
- Score: 9.191903314933915
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
Related papers
- A novel ANROA based control approach for grid-tied multi-functional
solar energy conversion system [0.0]
An adaptive control approach for a three-phase grid-interfaced solar photovoltaic system is proposed and discussed.
This method incorporates an Adaptive Neuro-fuzzy Inference System (ANFIS) with a Rain Optimization Algorithm (ROA)
Avoiding power quality problems including voltage fluctuations, harmonics, and flickers as well as unbalanced loads and reactive power usage is the major goal.
arXiv Detail & Related papers (2024-01-26T09:12:39Z) - Stability Bounds for Learning-Based Adaptive Control of Discrete-Time
Multi-Dimensional Stochastic Linear Systems with Input Constraints [3.8004168340068336]
We consider the problem of adaptive stabilization for discrete-time, multi-dimensional systems with bounded control input constraints and unbounded disturbances.
We propose a certainty-equivalent control scheme which combines online parameter estimation with saturated linear control.
arXiv Detail & Related papers (2023-04-02T16:38:13Z) - Formal Controller Synthesis for Markov Jump Linear Systems with
Uncertain Dynamics [64.72260320446158]
We propose a method for synthesising controllers for Markov jump linear systems.
Our method is based on a finite-state abstraction that captures both the discrete (mode-jumping) and continuous (stochastic linear) behaviour of the MJLS.
We apply our method to multiple realistic benchmark problems, in particular, a temperature control and an aerial vehicle delivery problem.
arXiv Detail & Related papers (2022-12-01T17:36:30Z) - Sparsity in Partially Controllable Linear Systems [56.142264865866636]
We study partially controllable linear dynamical systems specified by an underlying sparsity pattern.
Our results characterize those state variables which are irrelevant for optimal control.
arXiv Detail & Related papers (2021-10-12T16:41:47Z) - Probabilistic robust linear quadratic regulators with Gaussian processes [73.0364959221845]
Probabilistic models such as Gaussian processes (GPs) are powerful tools to learn unknown dynamical systems from data for subsequent use in control design.
We present a novel controller synthesis for linearized GP dynamics that yields robust controllers with respect to a probabilistic stability margin.
arXiv Detail & Related papers (2021-05-17T08:36:18Z) - Data-Driven Optimized Tracking Control Heuristic for MIMO Structures: A
Balance System Case Study [8.035375408614776]
The PID is illustrated on a two-input two-output balance system.
It integrates a self-adjusting nonlinear threshold with a neural network to compromise between the desired transient and steady state characteristics.
The neural network is trained upon optimizing a weighted-derivative like objective cost function.
arXiv Detail & Related papers (2021-04-01T02:00:20Z) - Gaussian Process-based Min-norm Stabilizing Controller for
Control-Affine Systems with Uncertain Input Effects and Dynamics [90.81186513537777]
We propose a novel compound kernel that captures the control-affine nature of the problem.
We show that this resulting optimization problem is convex, and we call it Gaussian Process-based Control Lyapunov Function Second-Order Cone Program (GP-CLF-SOCP)
arXiv Detail & Related papers (2020-11-14T01:27:32Z) - Learning Stabilizing Controllers for Unstable Linear Quadratic
Regulators from a Single Trajectory [85.29718245299341]
We study linear controllers under quadratic costs model also known as linear quadratic regulators (LQR)
We present two different semi-definite programs (SDP) which results in a controller that stabilizes all systems within an ellipsoid uncertainty set.
We propose an efficient data dependent algorithm -- textsceXploration -- that with high probability quickly identifies a stabilizing controller.
arXiv Detail & Related papers (2020-06-19T08:58:57Z) - Adaptive Control and Regret Minimization in Linear Quadratic Gaussian
(LQG) Setting [91.43582419264763]
We propose LqgOpt, a novel reinforcement learning algorithm based on the principle of optimism in the face of uncertainty.
LqgOpt efficiently explores the system dynamics, estimates the model parameters up to their confidence interval, and deploys the controller of the most optimistic model.
arXiv Detail & Related papers (2020-03-12T19:56:38Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.