Periodic optimal control, dissipativity and MPC

Recent research has established the importance of dissipativity for proving stability of economic MPC in the case of a steady state. In many cases, though, steady state operation is not economically optimal and periodic operation of the system yields a better performance. In this paper, we propose three different ways of extending the notion of dissipativity for periodic systems and illustrate them with three examples

A Gauss-Newton-Like Hessian Approximation for Economic NMPC

Economic Model Predictive Control (EMPC) has recently become popular because of its ability to control constrained nonlinear systems while explicitly optimizing a prescribed performance criterion. Large performance gains have been reported for many applications and closed-loop stability has been recently investigated. However, computational performance still remains an open issue and only few contributions have proposed real-time algorithms tailored to EMPC. We perform a step towards computationally cheap algorithms for EMPC by proposing a new positive-definite Hessian approximation which does not hinder fast convergence and is suitable for being used within the real-time iteration (RTI) scheme. We provide two simulation examples to demonstrate the effectiveness of RTI-based EMPC relying on the proposed Hessian approximation

Implications of discretization on dissipativity and economic model predictive control

© 2016 Elsevier LtdEconomic model predictive control, where a generic cost is employed as the objective function to be minimized, has recently gained much attention in model predictive control literature. Stability proof of the resulting closed-loop system is often based on strict dissipativity of the system with respect to the objective function. In this paper, starting with a continuous-time setup, we consider the ‘discretize then optimize’ approach to solving continuous-time optimal control problems and investigate the effect of the discretization process on the closed-loop system. We show that while the continuous-time system may be strictly dissipative with respect to the objective function, it is possible that the resulting closed-loop system is unstable if the discrete-approximation of the continuous-time optimal control problem is not properly set up. We use a popular example from the economic MPC literature to illustrate our results.This research is funded by the Federal Government of Nigeria through the Presidential Special Scholarship Scheme for Innovation and Development

Turnpike and dissipativity properties in dynamic real-time optimization and economic MPC

We investigate the turnpike and dissipativity properties of continuous-time optimal control problems. These properties play a key role in the analysis and design of schemes for dynamic real-time optimization and economic model predictive control. We show in a continuous-time setting that dissipativity of a system with respect to a steady state implies the existence of a turnpike at this steady state and optimal stationary operation at this steady state. Furthermore, we investigate the converse statements: We show that the existence of a turnpike at a steady state implies (a) that this steady state is the optimal steady state; and (b) that over an infinite horizon the system is optimally operated at this steady state. We draw upon a numerical example to illustrate our findings

Discrete-time Contraction Analysis and Controller Design for Nonlinear Processes

Shifting away from the traditional mass production approach, the process industry is moving towards more agile, cost-effective and dynamic process operation (next-generation smart plants). This warrants the development of control systems for nonlinear chemical processes to be capable of tracking time-varying setpoints to produce products with different specifications as per market demand and deal with variations in the raw materials and utility (e.g., energy). This thesis aims to develop controllers to achieve time-varying setpoints tracking using contraction theory. Through the differential dynamic system framework, the contraction conditions for discrete-time systems, which ensure the exponential convergence between system responses and feasible time-varying references, are derived. The discrete-time differential dissipativity condition is further developed, which can be used for disturbance rejection control designs. Computationally tractable equivalent conditions are then derived and additionally transformed into an Sum of Squares programming problem, such that a discrete-time control contraction metric and stabilising feedback controller can be jointly obtained. Synthesis and implementation details of the resulting contraction-based controller are provided, which can achieve offset-free tracking of feasible time-varying references. To do contraction analysis and control design for systems with uncertainties, which are often complex and difficult, neural networks are used. It involves training and constructing a neural network embedded contraction-based controller. Learning algorithms of uncertain system model parameters are developed. The resulting control scheme is capable of achieving efficient offset-free tracking of time-varying references, with a full range of model uncertainties, without the need for controller structure redesign as the reference or uncertain parameter changes. This neural network based approach also ensures process stability during online simultaneous control and learning of uncertain parameters. To further improve the economics of contraction-based controller, a nonlinear model predictive control approach is developed. Contraction condition is imposed as a constraint on the optimisation problem for model predictive control with an economic cost function, utilising Riemannian weighted graphs and shortest path techniques. The result is a reference flexible and fast optimal controller that can trade off between the rate of target trajectory convergence and economic benefit (away from the desired process objective)