B. De Schutter

Multi-agent model predictive control for transportation networks: Serial versus parallel schemes

We consider the control of large-scale transportation networks, like road traffic networks, power distribution networks, water distribution networks, etc. Control of these networks is often not possible from a single point by a single intelligent control agent; instead control has to be performed using multiple intelligent agents. We consider multi-agent control schemes in which each agent employs a model-based predictive control approach. Coordination between the agents is used to improve decision making. This coordination can be in the form of parallel or serial schemes. We propose a novel serial coordination scheme based on Lagrange theory and compare this with an existing parallel scheme. Experiments by means of simulations on a particular type of transportation network, viz., an electric power network, illustrate the performance of both schemes. It is shown that the serial scheme has preferable properties compared to the parallel scheme in terms of the convergence speed and the quality of the solution.

Robust output-feedback controller design via local BMI optimization

The problem of designing a globally optimal full-order output-feedback controller for polytopic uncertain systems is known to be a non-convex NP-hard optimization problem, that can be represented as a bilinear matrix inequality optimization problem for most design objectives. In this paper a new approach is proposed to the design of locally optimal controllers. It is iterative by nature, and starting from any initial feasible controller it performs local optimization over a suitably defined non-convex function at each iteration. The approach features the properties of computational efficiency, guaranteed convergence to a local optimum, and applicability to a very wide range of problems. Furthermore, a fast (but conservative) LMI-based procedure for computing an initially feasible controller is also presented. The complete approach is demonstrated on a model of one joint of a real-life space robotic manipulator.

Minimal state-space realization in linear system theory: an overview

We give a survey of the results in connection with the minimal state-space realization problem for linear time-invariant systems. We start with a brief historical overview and a short introduction to linear system theory. Next we present some of the basic algorithms for the reduction of nonminimal state-space realizations and for the minimal state-space realization of infinite or finite sequences of Markov parameters of linear time-invariant systems. Finally, we discuss some extensions of this problem to other classes of systems and point out some related problems.

Fast Model Predictive Control for Urban Road Networks via MILP

In this paper, an advanced control strategy, i.e., model predictive control (MPC), is applied to control and coordinate urban traffic networks. However, due to the nonlinearity of the prediction model, the optimization of MPC is a nonlinear nonconvex optimization problem. In this case, the online computational complexity becomes a big challenge for the MPC controller if it is implemented in a real-life traffic network. To overcome this problem, the online optimization problem is reformulated into a mixed-integer linear programming (MILP) optimization problem to increase the real-time feasibility of the MPC control strategy. The new optimization problem can be very efficiently solved by existing MILP solvers, and the global optimum of the problem is guaranteed. Moreover, we propose an approach to reduce the complexity of the MILP optimization problem even further. The simulation results show that the MILP-based MPC controllers can reach the same performance, but the time taken to solve the optimization becomes only a few seconds, which is a significant reduction, compared with the time required by the original MPC controller.

An ellipsoid algorithm for probabilistic robust controller design

Abstract In this paper, a new iterative approach to probabilistic robust controller design is presented, which is applicable to any robust controller/filter design problem that can be represented as an LMI feasibility problem. Recently, a probabilistic Subgradient Iteration algorithm was proposed for solving LMIs. It transforms the initial feasibility problem to an equivalent convex optimization problem, which is subsequently solved by means of an iterative algorithm. While this algorithm always converges to a feasible solution in a finite number of iterations, it requires that the radius of a non-empty ball contained into the solution set is known a priori. This rather restrictive assumption is released in this paper, while retaining the convergence property. Given an initial ellipsoid that contains the solution set, the approach proposed here iteratively generates a sequence of ellipsoids with decreasing volumes, all containing the solution set. At each iteration a random uncertainty sample is generated with a specified probability density, which parameterizes an LMI. For this LMI the next minimum-volume ellipsoid that contains the solution set is computed. An upper bound on the maximum number of possible correction steps, that can be performed by the algorithm before finding a feasible solution, is derived. A method for finding an initial ellipsoid containing the solution set, which is necessary for initialization of the optimization, is also given. The proposed approach is illustrated on a real-life diesel actuator benchmark model with real parametric uncertainty, for which a H 2 robust state-feedback controller is designed.

Adaptive Cruise Control for a SMART Car: A Comparison Benchmark for MPC-PWA Control Methods

The design of an adaptive cruise controller for a Smart car, a type of small car, is proposed as a benchmark setup for several model predictive control methods for nonlinear and piecewise affine systems. Each of these methods has been already applied to specific case studies, different from method to method. This paper has therefore the purpose of implementing and comparing them over a common benchmark, allowing us to assess the main properties, characteristics, and strong/weak points of each method. In the simulations, a realistic model of the Smart car, including gear box and engine nonlinearities, is considered. A description of the methods to be compared is presented, and the comparison results are collected in a table. In particular, the tradeoffs between complexity and accuracy of the solution, as well as computational aspects are highlighted.

Adaptive observers for TS fuzzy systems with unknown polynomial inputs

A large class of nonlinear systems can be well approximated by Takagi-Sugeno (TS) fuzzy models, with linear or affine consequents. However, in practical applications, the process under consideration may be affected by unknown inputs, such as disturbances, faults or unmodeled dynamics. In this paper, we consider the problem of simultaneously estimating the state and unknown inputs in TS systems. The inputs considered in this paper are (1) polynomials in time (such as a bias in the model or an unknown ramp input acting on the model) and (2) unmodeled dynamics. The proposed observer is designed based on the known part of the fuzzy model. Conditions on the asymptotic convergence of the observer are presented and the design guarantees an ultimate bound on the error signal. The results are illustrated on a simulation example.

A macroscopic traffic flow model for integrated control of freeway and urban traffic networks

We develop a macroscopic model for mixed urban and freeway traffic networks that is particularly suited for control purposes. In particular, we use an extended version of the METANET traffic flow model to describe the evolution of the traffic flows in the freeway part of the network. For the urban network we propose a new model that is based on the Kashani model. Furthermore, we also describe the interface between the urban and the freeway model. This results in an integrated model for mixed freeway and urban traffic networks. This model is especially suited for use in a model predictive traffic control approach.

MPC for continuous piecewise-affine systems

Abstract A large class of hybrid systems can be described by a max–min-plus-scaling (MMPS) model (i.e., using the operations maximization, minimization, addition and scalar multiplication). First, we show that continuous piecewise-affine systems are equivalent to MMPS systems. Next, we consider model predictive control (MPC) for these systems. In general, this leads to nonlinear, nonconvex optimization problems. We present a new MPC method for MMPS systems that is based on canonical forms for MMPS functions. In case the MPC constraints are linear constraints in the inputs only, this results in a sequence of linear optimization problems such that the MPC control can often be computed in a much more efficient way than by just applying nonlinear optimization as was done in previous work.

Kalman Filter-Based Distributed Predictive Control of Large-Scale Multi-Rate Systems: Application to Power Networks

In this paper, a novel distributed Kalman filter (KF) algorithm along with a distributed model predictive control (MPC) scheme for large-scale multi-rate systems is proposed. The decomposed multi-rate system consists of smaller subsystems with linear dynamics that are coupled via states. These subsystems are multi-rate systems in the sense that either output measurements or input updates are not available at certain sampling times. Such systems can arise, e.g., when the number of sensors is smaller than the number of variables to be controlled, or when measurements of outputs cannot be completed simultaneously because of practical limitations. The multi-rate nature gives rise to lack of information, which will cause uncertainty in the systems performance. To circumvent this problem, we propose a distributed KF-based MPC scheme, in which multiple control and estimation agents each determine actions for their own parts of the system. Via communication, the agents can in a cooperative way take one anothers actions into account. The main task of the proposed distributed KF is to compensate for the information loss due to the multi-rate nature of the systems by providing optimal estimation of the missing information. A demanding two-area power network example is used to demonstrate the effectiveness of the proposed method.