A computationally efficient robust tube based MPC for linear switched systems

Hariprasad, K.; Bhartiya, Sharad

doi:10.1016/j.nahs.2015.07.002

Cited by 21 publications

(12 citation statements)

References 25 publications

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“…In tube-based MPC [64] of constrained linear systems with bounded disturbances, the optimization problem (i.e., minimization of the cost for the nominal system) is separated from robustness issues by bounding the deviation from the nominal system by a sequence of invariant sets. A generalization of [64] to PWA systems is proposed in [65] under the rather restrictive assumption that a common Lyapunov function for the affine dynamics exists. The approach requires tightening of constraints and the online solution of a mixed integer program (MIP), where binary variables account for mode switching.…”

Section: Related Contributions On Pwa System Control Designmentioning

confidence: 99%

Set-based control for disturbed piecewise affine systems with state and actuation constraints

Schürmann

Vignali

Prandini

et al. 2020

Nonlinear Analysis: Hybrid Systems

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We address the finite horizon control of a discrete time piecewise affine (PWA) system, which is affected by an additive bounded disturbance. The goal is to robustly drive the state of the system to some target region, while satisfying state and actuation constraints. This problem is challenging due to the mixed discrete and continuous dynamics, requiring the exploration of many mode sequences. We address this problem by proposing a two-step approach which is based on designing a reference trajectory followed by a feedback controller that tries to make all solutions adhere to the reference mode sequence. As a result, the number of considered mode sequences can be drastically reduced. Termination is guaranteed since the time horizon and the number of modes are finite. Key to the computational efficiency of this procedure is the choice of the reference trajectory, which should be designed to avoid the branching of mode sequences from the reference sequence. The resulting set-based feedback control law is simple and easy to implement. Due to the use of reachability analysis, our results are formally correct. A quadrupletank benchmark example shows the effectiveness of our approach.

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Section: Related Contributions On Pwa System Control Designmentioning

confidence: 99%

Set-based control for disturbed piecewise affine systems with state and actuation constraints

Schürmann

Vignali

Prandini

et al. 2020

Nonlinear Analysis: Hybrid Systems

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show abstract

“…The finite-time optimal controller has to account for possible switches and the set of initial states is generally non-convex, making it costly to find explicit offline solutions [7], [8], [14], [23]. Guaranteeing recursive feasibility and Lyapunov stability in the receding-horizon implementation requires a terminal invariant set and a CLF on that set [13], [24], [25]. If the closed-loop equilibrium is a shared point of some regions, finding such a CLF is non-trivial and needs the methods of [4], [5], [9], [12], [22], bringing once again the issues of the S-procedure, and initialization, and respecting constraints.…”

Section: Introductionmentioning

confidence: 99%

Systematic Stabilization of Constrained Piecewise Affine Systems

Reza¹,

Bridgeman²

2022

Preprint

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This paper presents an efficient, offline method to simultaneously synthesize controllers and seek closed-loop Lyapunov functions for constrained piecewise affine systems on triangulated subsets of the admissible states. Triangulation refinements explore a rich class of controllers and Lyapunov functions. Since an explicit Lipschitz Lyapunov function is found, an invariant subset of the closed-loop region of attraction is obtained. Moreover, it is a control Lyapunov function, so minimum-norm controllers can be realized through online quadratic programming. It is formulated as a sequence of semidefinite programs. The method avoids computationally burdensome non-convex optimizations and a-priori design choices that are typical of similar existing methods.

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“…Model-based control approaches are popularly being used for batch process control [1,2,3,4,5]. Model predictive control is an advanced control strategy extensively used in the process industries [6,7] and employs mathematical programming to solve a constrained, possibly non-convex, optimisation problem.…”

Section: Introductionmentioning

confidence: 99%

TASAC: a twin-actor reinforcement learning framework with stochastic policy for batch process control

Joshi¹,

Kodamanaa²,

Kandath³

et al. 2022

Preprint

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Due to their complex nonlinear dynamics and batch-to-batch variability, batch processes pose a challenge for process control. Due to the absence of accurate models and resulting plant-model mismatch, these problems become harder to address for advanced model-based control strategies. Reinforcement Learning (RL), wherein an agent learns the policy by directly interacting with the environment, offers a potential alternative in this context. RL frameworks with actor-critic architecture have recently become popular for controlling systems where state and action spaces are continuous. It has been shown that an ensemble of actor and critic networks further helps the agent learn better policies due to the enhanced exploration due to simultaneous policy learning. To this end, the current study proposes a stochastic actor-critic RL algorithm, termed Twin Actor Soft Actor-Critic (TASAC), by incorporating an ensemble of actors for learning, in a maximum entropy framework, for batch process control.

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A computationally efficient robust tube based MPC for linear switched systems

Cited by 21 publications

References 25 publications

Set-based control for disturbed piecewise affine systems with state and actuation constraints

Set-based control for disturbed piecewise affine systems with state and actuation constraints

Systematic Stabilization of Constrained Piecewise Affine Systems

TASAC: a twin-actor reinforcement learning framework with stochastic policy for batch process control

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