A parsimonious algorithm for the solution of continuous-time constrained LQR problems with guaranteed convergence

Polyhedral control Lyapunov functions (PCLFs) are exploited in this paper to propose a linear model predictive control (MPC) formulation that guarantees a “large” domain of attraction (DoA) even for short horizon. In particular, the terminal region of the proposed finite-horizon MPC formulation is chosen as a level set of an appropriate PCLF. For small dimensional systems, this terminal region can be explicitly computed as an arbitrarily close approximation to the entire (infinite-horizon) stabilizable set. Global stability of the origin is guaranteed by using an “inflated” PCLF as terminal cost. The proposed MPC scheme can be formulated as a (small dimensional) quadratic programming problem by introducing one additional scalar variable. Numerical examples show the main benefits and achievements of the proposed formulation in terms of trade-off between volume of the DoA, computational time and closed-loop performance

Population Monte Carlo algorithms

We give a cross-disciplinary survey on ``population'' Monte Carlo algorithms. In these algorithms, a set of ``walkers'' or ``particles'' is used as a representation of a high-dimensional vector. The computation is carried out by a random walk and split/deletion of these objects. The algorithms are developed in various fields in physics and statistical sciences and called by lots of different terms -- ``quantum Monte Carlo'', ``transfer-matrix Monte Carlo'', ``Monte Carlo filter (particle filter)'',``sequential Monte Carlo'' and ``PERM'' etc. Here we discuss them in a coherent framework. We also touch on related algorithms -- genetic algorithms and annealed importance sampling.Comment: Title is changed (Population-based Monte Carlo -> Population Monte Carlo). A number of small but important corrections and additions. References are also added. Original Version is read at 2000 Workshop on Information-Based Induction Sciences (July 17-18, 2000, Syuzenji, Shizuoka, Japan). No figure

Nonparametric nonlinear model predictive control

Model Predictive Control (MPC) has recently found wide acceptance in industrial applications, but its potential has been much impeded by linear models due to the lack of a similarly accepted nonlinear modeling or databased technique. Aimed at solving this problem, the paper addresses three issues: (i) extending second-order Volterra nonlinear MPC (NMPC) to higher-order for improved prediction and control; (ii) formulating NMPC directly with plant data without needing for parametric modeling, which has hindered the progress of NMPC; and (iii) incorporating an error estimator directly in the formulation and hence eliminating the need for a nonlinear state observer. Following analysis of NMPC objectives and existing solutions, nonparametric NMPC is derived in discrete-time using multidimensional convolution between plant data and Volterra kernel measurements. This approach is validated against the benchmark van de Vusse nonlinear process control problem and is applied to an industrial polymerization process by using Volterra kernels of up to the third order. Results show that the nonparametric approach is very efficient and effective and considerably outperforms existing methods, while retaining the original data-based spirit and characteristics of linear MPC

Efficient Nonlinear Programming Algorithms for Chemical Process Control and Operations

Nonlinear programming (NLP) has been a key enabling tool for model-based decision-making in the chemical industry for over 50 years. Opti-mization is frequently applied in numerous ar-eas of chemical engineering including the de-velopment of process models from experimen-tal data, design of process flowsheets and equip-ment, planning and scheduling of chemical pro-cess operations, and the analysis of chemical pro-cesses under uncertainty and adverse conditions. These off-line tasks frequently require the solu-tion of NLPs formulated with detailed, lareg-scale process models. More recently, these tasks are complemented by time-critical, on-line optimization problem

Optimal control of constrained, piecewise affine systems with bounded disturbances

Published versio