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Register a new userPredictive Optimal Control with Data-Based Disturbance Scenario Tree Approximation
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Efficiently computing the optimal control policy concerning a complicated future with stochastic disturbance has always been a challenge. The predicted stochastic future disturbance can be represented by a scenario tree, but solving the optimal control problem with a scenario tree is usually computationally demanding. In this paper, we propose a data-based clustering approximation method for the scenario tree representation. Differently from the popular Markov chain approximation, the proposed method can retain information from previous steps while keeping the state space size small. Then the predictive optimal control problem can be approximately solved with reduced computational load using dynamic programming. The proposed method is evaluated in numerical examples and compared with the method which considers the disturbance as a non-stationary Markov chain. The results show that the proposed method can achieve better control performance than the Markov chain method.
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Appropriate greenhouse temperature should be maintained to ensure crop production while minimizing energy consumption. Even though weather forecasts could provide a certain amount of information to improve control performance, it is not perfect and forecast error may cause the temperature to deviate from the acceptable range. To inherent uncertainty in weather that affects control accuracy, this paper develops a data-driven robust model predictive control (MPC) approach for greenhouse temperature control. The dynamic model is obtained from thermal resistance-capacitance modeling derived by the Building Resistance-Capacitance Modeling (BRCM) toolbox. Uncertainty sets of ambient temperature and solar radiation are captured by support vector clustering technique, and they are further tuned for better quality by training-calibration procedure. A case study that implements the carefully chosen uncertainty sets on robust model predictive control shows that the data-driven robust MPC has better control performance compared to rule-based control, certainty equivalent MPC, and robust MPC.
The rapidly growing use of lithium-ion batteries across various industries highlights the pressing issue of optimal charging control, as charging plays a crucial role in the health, safety and life of batteries. The literature increasingly adopts model predictive control (MPC) to address this issue, taking advantage of its capability of performing optimization under constraints. However, the computationally complex online constrained optimization intrinsic to MPC often hinders real-time implementation. This paper is thus proposed to develop a framework for real-time charging control based on explicit MPC (eMPC), exploiting its advantage in characterizing an explicit solution to an MPC problem, to enable real-time charging control. The study begins with the formulation of MPC charging based on a nonlinear equivalent circuit model. Then, multi-segment linearization is conducted to the original model, and applying the eMPC design to the obtained linear models leads to a charging control algorithm. The proposed algorithm shifts the constrained optimization to offline by precomputing explicit solutions to the charging problem and expressing the charging law as piecewise affine functions. This drastically reduces not only the online computational costs in the control run but also the difficulty of coding. Extensive numerical simulation and experimental results verify the effectiveness of the proposed eMPC charging control framework and algorithm. The research results can potentially meet the needs for real-time battery management running on embedded hardware.
We propose Kernel Predictive Control (KPC), a learning-based predictive control strategy that enjoys deterministic guarantees of safety. Noise-corrupted samples of the unknown system dynamics are used to learn several models through the formalism of non-parametric kernel regression. By treating each prediction step individually, we dispense with the need of propagating sets through highly non-linear maps, a procedure that often involves multiple conservative approximation steps. Finite-sample error bounds are then used to enforce state-feasibility by employing an efficient robust formulation. We then present a relaxation strategy that exploits on-line data to weaken the optimization problem constraints while preserving safety. Two numerical examples are provided to illustrate the applicability of the proposed control method.
Stochastic model predictive control (SMPC) has been a promising solution to complex control problems under uncertain disturbances. However, traditional SMPC approaches either require exact knowledge of probabilistic distributions, or rely on massive scenarios that are generated to represent uncertainties. In this paper, a novel scenario-based SMPC approach is proposed by actively learning a data-driven uncertainty set from available data with machine learning techniques. A systematical procedure is then proposed to further calibrate the uncertainty set, which gives appropriate probabilistic guarantee. The resulting data-driven uncertainty set is more compact than traditional norm-based sets, and can help reducing conservatism of control actions. Meanwhile, the proposed method requires less data samples than traditional scenario-based SMPC approaches, thereby enhancing the practicability of SMPC. Finally the optimal control problem is cast as a single-stage robust optimization problem, which can be solved efficiently by deriving the robust counterpart problem. The feasibility and stability issue is also discussed in detail. The efficacy of the proposed approach is demonstrated through a two-mass-spring system and a building energy control problem under uncertain disturbances.
We propose a learning-based, distributionally robust model predictive control approach towards the design of adaptive cruise control (ACC) systems. We model the preceding vehicle as an autonomous stochastic system, using a hybrid model with continuous dynamics and discrete, Markovian inputs. We estimate the (unknown) transition probabilities of this model empirically using observed mode transitions and simultaneously determine sets of probability vectors (ambiguity sets) around these estimates, that contain the true transition probabilities with high confidence. We then solve a risk-averse optimal control problem that assumes the worst-case distributions in these sets. We furthermore derive a robust terminal constraint set and use it to establish recursive feasibility of the resulting MPC scheme. We validate the theoretical results and demonstrate desirable properties of the scheme through closed-loop simulations.
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