Support Vector Machine Informed Explicit Nonlinear Model Predictive Control Using Low-Discrepancy Sequences

Chakrabarty, Ankush; Dinh, Vu; Corless, Martin; Rundell, Ann E.; Żak, Stanisław H.; Buzzard, Gregery T.

doi:10.1109/tac.2016.2539222

Cited by 68 publications

(47 citation statements)

References 50 publications

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“…Since our initial Lyapunov function is quadratic, we include the quadratic terms of the components of x to be in the basis ψpxq. Then we can express the initial Lyapunov function x J P x obtained by solving (24) with appropriate weights in the ψpxq, respectively, setting all other weights to be zero. With the approximator initialized as above, the policy evaluation step (18a) is replaced by…”

Section: A Unconstrained Adpmentioning

confidence: 99%

“…Note that the conditions (24) and (31) are LMIs in S, Y , and ν for a fixedL φ . Therefore one can maximize the volume of E P by solving a constrained convex program with cost function´log |S| (the log-determinant of S) subject to the constraints (24) and (31) while line searching for α. This will reduce the conservativeness of the domain of attraction.…”

Section: B Input-constrained Adp With Safetymentioning

confidence: 99%

“…For example, the class of Lipschitz nonlinearities (which constitute a large share of nonlinearities observed in applications) can be described using only a few parameters: the Lipschitz constants of the nonlinear components. Recent work has investigated the utility of Lipschitz properties in constructing controllers when an oracle is available [24] or in designing models for prediction [25] with on-line data used for controller refinement [26] In this paper, we construct control policies that respect constraints and certify stability (with high probability) for applications where only off-line data is available, and no oracle is present. We do so through the systematic use of multiplier matrices that enable the representation of nonlinear dynamics through quadratic constraints [27], [28] without requiring knowledge of the underlying nonlinearity.…”

Section: Introductionmentioning

confidence: 99%

“…Require: Termination condition constant ac Require: Historical data D 1: Estimate Lipschitz constantL φ using Algorithm 1 Require: Compute stabilizing control gain K0 via SDP(24) 2: Fix safe initial control policy u0pxq " K0x 3: while }J k´Jk´1 } ě ac do…”

mentioning

confidence: 99%

See 3 more Smart Citations

Safe Approximate Dynamic Programming via Kernelized Lipschitz Estimation

Chakrabarty

Jha

Buzzard

et al. 2021

IEEE Trans. Neural Netw. Learning Syst.

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We develop a method for obtaining safe initial policies for reinforcement learning via approximate dynamic programming (ADP) techniques for uncertain systems evolving with discrete-time dynamics. We employ kernelized Lipschitz estimation and semidefinite programming for computing admissible initial control policies with provably high probability. Such admissible controllers enable safe initialization and constraint enforcement while providing exponential stability of the equilibrium of the closed-loop system.

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Section: A Unconstrained Adpmentioning

confidence: 99%

Section: B Input-constrained Adp With Safetymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Safe Approximate Dynamic Programming via Kernelized Lipschitz Estimation

Chakrabarty

Jha

Buzzard

et al. 2021

IEEE Trans. Neural Netw. Learning Syst.

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“…Very recently, Chakrabarty et al . proposed a low‐complexity deterministic learning method for estimating the feasible region of explicit NMPC with SVC . Whereas, a major difference of our work from the foregoing works is that we propose a unified explicit optimal controller with global robustness through approximating the piecewise affine control law of EMPC with SVR rather than estimating the feasible space.…”

Section: Introductionmentioning

confidence: 99%

Globally robust explicit model predictive control of constrained systems exploiting SVM‐based approximation

Wei

Luo

Dai

et al. 2016

Intl J Robust & Nonlinear

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Summary This paper presents a systematic method to address the reduction of online computational complexity and infeasibility problem of explicit model predictive control for constrained systems under external disturbance. In feasible state space, in order to avoid the expensive database searching procedure, support vector machine‐based approximation is proposed to yield a novel unified explicit optimal control law rather than a piecewise affine one developed by explicit model predictive control. In infeasible state space, through constructing finite maximum control invariant sets around fictitious equilibrium points, a reachable controller is devised to steer the infeasible state asymptotically to the feasible state space without violating the hard constraint. Consequently, global robustness is guaranteed by introducing a minimum robust positively invariant set by means of the tube‐based technique, despite the coexistence of external disturbance and training error. Finally, the performance of the presently proposed control law is evaluated through three groups of numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.

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Lyapunov‐based EMPC of constrained nonlinear systems with changing economic costs

2020

Asian Journal of Control

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There exist frequent economic cost changes in many process systems due to variations in price, market demand, disturbance, etc. This change switches the economic setpoint of processes throughout their operation and may cause a loss of feasibility and/or stability in economic model predictive control (EMPC). In this paper, we present a novel Lyapunov-based EMPC scheme for optimization of changing economic costs of constrained nonlinear systems.

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Support Vector Machine Informed Explicit Nonlinear Model Predictive Control Using Low-Discrepancy Sequences

Cited by 68 publications

References 50 publications

Safe Approximate Dynamic Programming via Kernelized Lipschitz Estimation

Safe Approximate Dynamic Programming via Kernelized Lipschitz Estimation

Globally robust explicit model predictive control of constrained systems exploiting SVM‐based approximation

Lyapunov‐based EMPC of constrained nonlinear systems with changing economic costs

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