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.
The paper is organised as follows. Following the introduction, the target computational platform is described in . An approach for formulating predictive controller design as an optimization problem is presented in . Possible ways of formalising design objectives and constraints are discussed within the section. Following that, reviews existing algorithms for solving the resulting optimization problem and justifies using the BiMADS algorithm @cite_25 for solving MPC design problems. Two case studies are considered in : design of CPU-based and FPGA-based implementations of a fast gradient-based predictive controller. concludes the paper.
@cite_25
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This paper formulates the vehicle navigation task as a constrained optimal control problem with constraints bounding a traversable region of the environment. A model predictive controller iteratively plans an optimal vehicle trajectory through the constrained corridor and uses this trajectory to establish the minimum threat posed to the vehicle given its current state and driver inputs. Based on this threat assessment, the level of controller intervention required to prevent departure from the traversable corridor is calculated and driver controller inputs are scaled accordingly. Simulated and experimental results are presented to demonstrate multiple threat metrics and configurable intervention laws. 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. This paper addresses the attraction domain of model-based predictive control (MPC) for nonlinear systems with control input and state constraints. Based on a stability condition of nonlinear MPC, a method to determine the terminal weighting term in the performance index and the terminal stabilising control law to maximise the domain of attraction of the nonlinear MPC is proposed. The problem of maximisation of the attraction region is recast as a well-defined optimisation problem. By an LMI based optimisation approach, the terminal weighting item and fictitious terminal stabilising control law axe optimised to enlarge the attraction domain and hence the feasibility domain of the nonlinear MPC method. The proposed method is illustrated by a numerical example and favourably compared with existing results. This paper proposes a novel two-stage optimization method for robust model predictive control (RMPC) with Gaussian disturbance and state estimation error. Since the disturbance is unbounded, it is impossible to achieve zero probability of violating constraints. Our goal is to optimize the expected value of an objective function while limiting the probability of violating any constraints over the planning horizon (joint chance constraint). Prior arts include ellipsoidal relaxation approach [1] and particle control [2], but the former yields very conservative result and the latter is computationally intensive. Our approach divide the optimization problem into two stages; the upper-stage that optimizes risk allocation, and the lower-stage that optimizes control sequence with tightened constraints. The lower-stage is a regular convex optimization, such as linear programming or quadratic programming. The upper-stage is also convex, but the objective function is not always differentiable. We developed a fast descent algorithm for the upper-stage called iterative risk allocation (IRA), which yield much smaller suboptimality than ellipsoidal relaxation method while achieving a substantial speedup compared to and particle control.