| 1. |
- Dai, L., et al.
(författare)
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Distributed stochastic MPC for systems with parameter uncertainty and disturbances
- 2018
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Ingår i: International Journal of Robust and Nonlinear Control. - : John Wiley and Sons Ltd. - 1049-8923 .- 1099-1239. ; 28:6, s. 2424-2441
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Tidskriftsartikel (refereegranskat)abstract
- A distributed stochastic model predictive control algorithm is proposed for multiple linear subsystems with both parameter uncertainty and stochastic disturbances, which are coupled via probabilistic constraints. To handle the probabilistic constraints, the system dynamics is first decomposed into a nominal part and an uncertain part. The uncertain part is further divided into 2 parts: the first one is constrained to lie in probabilistic tubes that are calculated offline through the use of the probabilistic information on disturbances, whereas the second one is constrained to lie in polytopic tubes whose volumes are optimized online and whose facets' orientations are determined offline. By permitting a single subsystem to optimize at each time step, the probabilistic constraints are then reduced into a set of linear deterministic constraints, and the online optimization problem is transformed into a convex optimization problem that can be performed efficiently. Furthermore, compared to a centralized control scheme, the distributed stochastic model predictive control algorithm only requires message transmissions when a subsystem is optimized, thereby offering greater flexibility in communication. By designing a tailored invariant terminal set for each subsystem, the proposed algorithm can achieve recursive feasibility, which, in turn, ensures closed-loop stability of the entire system. A numerical example is given to illustrate the efficacy of the algorithm. Copyright
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| 2. |
- Dai, L., et al.
(författare)
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Stochastic self-triggered model predictive control for linear systems with probabilistic constraints
- 2018
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Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 92, s. 9-17
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Tidskriftsartikel (refereegranskat)abstract
- A stochastic self-triggered model predictive control (SSMPC) algorithm is proposed for linear systems subject to exogenous disturbances and probabilistic constraints. The main idea behind the self-triggered framework is that at each sampling instant, an optimization problem is solved to determine both the next sampling instant and the control inputs to be applied between the two sampling instants. Although the self-triggered implementation achieves communication reduction, the control commands are necessarily applied in open-loop between sampling instants. To guarantee probabilistic constraint satisfaction, necessary and sufficient conditions are derived on the nominal systems by using the information on the distribution of the disturbances explicitly. Moreover, based on a tailored terminal set, a multi-step open-loop MPC optimization problem with infinite prediction horizon is transformed into a tractable quadratic programming problem with guaranteed recursive feasibility. The closed-loop system is shown to be stable. Numerical examples illustrate the efficacy of the proposed scheme in terms of performance, constraint satisfaction, and reduction of both control updates and communications with a conventional time-triggered scheme.
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| 3. |
- Gao, Yulong
(författare)
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Stochastic Invariance and Aperiodic Control for Uncertain Constrained Systems
- 2018
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Uncertainties and constraints are present in most control systems. For example, robot motion planning and building climate regulation can be modeled as uncertain constrained systems. In this thesis, we develop mathematical and computational tools to analyze and synthesize controllers for such systems.As our first contribution, we characterize when a set is a probabilistic controlled invariant set and we develop tools to compute such sets. A probabilistic controlled invariantset is a set within which the controller is able to keep the system state with a certainprobability. It is a natural complement to the existing notion of robust controlled invariantsets. We provide iterative algorithms to compute a probabilistic controlled invariantset within a given set based on stochastic backward reachability. We prove that thesealgorithms are computationally tractable and converge in a finite number of iterations. The computational tools are demonstrated on examples of motion planning, climate regulation, and model predictive control.As our second contribution, we address the control design problem for uncertain constrained systems with aperiodic sensing and actuation. Firstly, we propose a stochastic self-triggered model predictive control algorithm for linear systems subject to exogenous disturbances and probabilistic constraints. We prove that probabilistic constraint satisfaction, recursive feasibility, and closed-loop stability can be guaranteed. The control algorithm is computationally tractable as we are able to reformulate the problem into a quadratic program. Secondly, we develop a robust self-triggered control algorithm for time-varying and uncertain systems with constraints based on reachability analysis. In the particular case when there is no uncertainty, the design leads to a control system requiring minimum number of samples over finite time horizon. Furthermore, when the plant is linear and the constraints are polyhedral, we prove that the previous algorithms can be reformulated as mixed integer linear programs. The method is applied to a motion planning problem with temporal constraints.
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| 4. |
- Gao, Yulong, et al.
(författare)
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Stochastic Optimal Control of Dynamic Queue Systems : A Probabilistic Perspective
- 2018
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Ingår i: 2018 15TH INTERNATIONAL CONFERENCE ON CONTROL, AUTOMATION, ROBOTICS AND VISION (ICARCV). - : IEEE. - 9781538695821 ; , s. 837-842
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Konferensbidrag (refereegranskat)abstract
- Queue overflow of a dynamic queue system gives rise to the information loss (or packet loss) in the communication buffer or the decrease of throughput in the transportation network. This paper investigates a stochastic optimal control problem for dynamic queue systems when imposing probability constraints on queue overflows. We reformulate this problem as a Markov decision process (MDP) with safety constraints. We prove that both finite-horizon and infinite-horizon stochastic optimal control for MDP with such constraints can be transformed as a linear program (LP), respectively. Feasibility conditions are provided for the finite-horizon constrained control problem. Two implementation algorithms are designed under the assumption that only the state (not the state distribution) can be observed at each time instant. Simulation results compare optimal cost and state distribution among different scenarios, and show the probability constraint satisfaction by the proposed algorithms.
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