No Arabic abstract
This paper introduces HPIPM, a high-performance framework for quadratic programming (QP), designed to provide building blocks to efficiently and reliably solve model predictive control problems. HPIPM currently supports three QP types, and provides interior point method (IPM) solvers as well (partial) condensing routines. In particular, the IPM for optimal control QPs is intended to supersede the HPMPC solver, and it largely improves robustness while keeping the focus on speed. Numerical experiments show that HPIPM reliably solves challenging QPs, and that it outperforms other state-of-the-art solvers in speed.
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.
Move blocking (MB) is a widely used strategy to reduce the degrees of freedom of the Optimal Control Problem (OCP) arising in receding horizon control. The size of the OCP is reduced by forcing the input variables to be constant over multiple discretization steps. In this paper, we focus on developing computationally efficient MB schemes for multiple shooting based nonlinear model predictive control (NMPC). The degrees of freedom of the OCP is reduced by introducing MB in the shooting step, resulting in a smaller but sparse OCP. Therefore, the discretization accuracy and level of sparsity is maintained. A condensing algorithm that exploits the sparsity structure of the OCP is proposed, that allows to reduce the computation complexity of condensing from quadratic to linear in the number of discretization nodes. As a result, active-set methods with warm-start strategy can be efficiently employed, thus allowing the use of a longer prediction horizon. A detailed comparison between the proposed scheme and the nonuniform grid NMPC is given. Effectiveness of the algorithm in reducing computational burden while maintaining optimization accuracy and constraints fulfillment is shown by means of simulations with two different problems.
In this paper, we propose a chance constrained stochastic model predictive control scheme for reference tracking of distributed linear time-invariant systems with additive stochastic uncertainty. The chance constraints are reformulated analytically based on mean-variance information, where we design suitable Probabilistic Reachable Sets for constraint tightening. Furthermore, the chance constraints are proven to be satisfied in closed-loop operation. The design of an invariant set for tracking complements the controller and ensures convergence to arbitrary admissible reference points, while a conditional initialization scheme provides the fundamental property of recursive feasibility. The paper closes with a numerical example, highlighting the convergence to changing output references and empirical constraint satisfaction.
To provide automatic generation control (AGC) service, wind farms (WFs) are required to control their operation dynamically to track the time-varying power reference. Wake effects impose significant aerodynamic interactions among turbines, which remarkably influence the WF dynamic power production. The nonlinear and high-dimensional nature of dynamic wake model, however, brings extremely high computation complexity and obscure the design of WF controllers. This paper overcomes the control difficulty brought by the dynamic wake model by proposing a novel control-oriented reduced order WF model and a deep-learning-aided model predictive control (MPC) method. Leveraging recent advances in computational fluid dynamics (CFD) to provide high-fidelity data that simulates WF dynamic wake flows, two novel deep neural network (DNN) architectures are specially designed to learn a dynamic WF reduced-order model (ROM) that can capture the dominant flow dynamics. Then, a novel MPC framework is constructed that explicitly incorporates the obtained WF ROM to coordinate different turbines while considering dynamic wake interactions. The proposed WF ROM and the control method are evaluated in a widely-accepted high-dimensional dynamic WF simulator whose accuracy has been validated by realistic measurement data. A 9-turbine WF case and a larger 25-turbine WF case are studied. By reducing WF model states by many orders of magnitude, the computational burden of the control method is reduced greatly. Besides, through the proposed method, the range of AGC signals that can be tracked by the WF in the dynamic operation is extended compared with the existing greedy controller.
For controller design for systems on manifolds embedded in Euclidean space, it is convenient to utilize a theory that requires a single global coordinate system on the ambient Euclidean space rather than multiple local charts on the manifold or coordinate-free tools from differential geometry. In this article, we apply such a theory to design model predictive tracking controllers for systems whose dynamics evolve on manifolds and illustrate its efficacy with the fully actuated rigid body attitude control system.