Model predictive control (MPC) is a computationally demanding control technique that allows dealing with multiple-input and multiple-output systems while handling constraints in a systematic way. The necessity of solving an optimization problem at every sampling instant often 1) limits the application scope to slow dynamical systems and or 2) results in expensive computational hardware implementations. Traditional MPC design is based on the manual tuning of software and computational hardware design parameters, which leads to suboptimal implementations. This brief proposes a framework for automating the MPC software and computational hardware codesign while achieving an optimal tradeoff between computational resource usage and controller performance. The proposed approach is based on using a biobjective optimization algorithm, namely BiMADS. Two test studies are considered: a central processing unit and field-programmable gate array implementations of fast gradient-based MPC. Numerical experiments show that the optimization-based design outperforms Latin hypercube sampling, a statistical sampling-based design exploration technique.
Model predictive controller design is a multidisciplinary problem that involves tuning several coupled design parameters. Traditionally MPC controllers were tuned manually, with a trial and error approach, which cannot be considered as a viable option for most present-day applications, considering the number of design parameters and design evaluation time @cite_29 . Moreover, manual tuning often requires understanding the nature of the controlled dynamical system and MPC controller with the underlying optimization solver. Available tuning guidelines for model predictive control, including heuristic and systematic (but not automatic) approaches, are reviewed in @cite_15 . Note that only high level optimal control problem parameters (e.g. horizon length, weights on states inputs) are considered in the review paper, without regard to solving the underlying optimization problem.
@cite_29 @cite_15
2016211524 2790404719 2963165111 2887531520
More than 15 years after model predictive control (MPC) appeared in industry as an effective means to deal with multivariable constrained control problems, a theoretical basis for this technique has started to emerge. The issues of feasibility of the on-line optimization, stability and performance are largely understood for systems described by linear models. Much progress has been made on these issues for non-linear systems but for practical applications many questions remain, including the reliability and efficiency of the on-line computation scheme. To deal with model uncertainty ‘rigorously’ an involved dynamic programming problem must be solved. The approximation techniques proposed for this purpose are largely at a conceptual stage. Among the broader research needs the following areas are identified: multivariable system identification, performance monitoring and diagnostics, non-linear state estimation, and batch system control. Many practical problems like control objective prioritization and symptom-aided diagnosis can be integrated systematically and effectively into the MPC framework by expanding the problem formulation to include integer variables yielding a mixed-integer quadratic or linear program. Efficient techniques for solving these problems are becoming available. Model Predictive Control (MPC) plays an important role in optimizing operations of complex cyber-physical systems because of its ability to forecast system’s behavior and act under system level constraints. However, MPC requires reasonably accurate underlying models of the system. In many applications, such as building control for energy management, Demand Response, or peak power reduction, obtaining a high-fidelity physics-based model is cost and time prohibitive, thus limiting the widespread adoption of MPC. To this end, we propose a data-driven control algorithm for MPC that relies only on the historical data. We use multi-output regression trees to represent the system’s dynamics over multiple future time steps and formulate a finite receding horizon control problem that can be solved in real-time in closed-loop with the physical plant. We apply this algorithm to peak power reduction in buildings to optimally trade-off peak power reduction against thermal comfort without having to learn white grey box models of the systems dynamics. Model predictive control (MPC) is a popular control method that has proved effective for robotics, among other fields. MPC performs re-planning at every time step. Re-planning is done with a limited horizon per computational and real-time constraints and often also for robustness to potential model errors. However, the limited horizon leads to suboptimal performance. In this work, we consider the iterative learning setting, where the same task can be repeated several times, and propose a policy improvement scheme for MPC. The main idea is that between executions we can, offline, run MPC with a longer horizon, resulting in a hindsight plan. To bring the next real-world execution closer to the hindsight plan, our approach learns to re-shape the original cost function with the goal of satisfying the following property: short horizon planning (as realistic during real executions) with respect to the shaped cost should result in mimicking the hindsight plan. This effectively consolidates long-term reasoning into the short-horizon planning. We empirically evaluate our approach in contact-rich manipulation tasks both in simulated and real environments, such as peg insertion by a real PR2 robot. In this paper, we present a novel constraint tightening approach for nonlinear robust model predictive control (MPC). This approach uses a simple constructive constraint tightening based on growing tubes. Contrary to other approaches, we require no complex offline computations to obtain a stabilizing control law. Instead, we consider the notion of incremental stabilizability and design tubes based on an estimate of the achievable exponential decay rate. In addition, we show how this tightening can be used as an ad-hoc modification to improve the robustness of MPC without terminal constraints. We study the system theoretic properties of the resulting closed-loop system, including bounds on the region of attraction and the minimal robust positively invariant (RPI) set. Within an MPC framework without terminal constraints, the proposed constraint tightening leads to a nonlinear robust controller without complex design procedures, which makes it appealing for practical applications.