Fault-tolerant aspects of MPC

The various aspects of fault-tolerant control systems that have the ability to survive major equipment failures or damages are discussed. Model predictive control (MPC) offers a promising basis for fault-tolerant control. Failures can be dealt with by updating internal models and letting the on-line optimizer control the system in its new condition. Fault detection and isolation (FDI) and the management of complex models are two emerging technologies in this field.

Verifying stability of approximate explicit MPC

Several authors have proposed algorithms for approximate explicit MPC [1],[2],[3]. These algorithms have in common that they develop a stability criterion for approximate explicit MPC that require the approximate cost function to be within a certain distance from the optimal cost function. In this paper, stability is instead ascertained by considering only the cost function of the approximate MPC. If a region of the state space is found where the cost function is not decreasing, this indicates that an improved approximation (to the optimal control) is required in that region. If the approximate cost function is decreasing everywhere, no further refinement of the approximate MPC is necessary, since stability is guaranteed. ©2009 IEEE.

Embedded Model Predictive Control (MPC) using a FPGA

Model Predictive Control (MPC) is increasingly being proposed for application to miniaturized devices, fast and/or embedded systems. A major obstacle to this is its computation time requirement. Continuing our previous studies of implementing constrained MPC on Field Programmable Gate Arrays (FPGA), this paper begins to exploit the possibilities of parallel computation, with the aim of speeding up the MPC implementation. Simulation studies on a realistic example show that it is possible to implement constrained MPC on an FPGA chip with a 25MHz clock and achieve MPC implementation rates comparable to those achievable on a Pentium 3.0 GHz PC. Copyright © 2007 International Federation of Automatic Control All Rights Reserved.

Robust variable horizon MPC with move blocking

This paper introduces a new formulation of variable horizon model predictive control (VH-MPC) that utilises move blocking for reducing computational complexity. Various results pertaining to move blocking are derived, following which, a generalised blocked VH-MPC controller is formulated for linear discrete-time systems. Robustness to bounded disturbances is ensured through the use of tightened constraints. The resulting time-varying control scheme is shown to guarantee robust recursive feasibility and finite-time completion. An example is then presented for a particular choice of blocking regime, as would be applicable to vehicle manœuvring problems. Simulations demonstrate the efficacy of the formulation. © 2012 Elsevier B.V. All rights reserved.

Robust multiplexed MPC for distributed multi-agent systems

This paper extends the authors' earlier work which adapted robust multiplexed MPC for application to distributed control of multi-agent systems with non-interacting dynamics and coupled constraint sets in the presence of persistent unknown, but bounded disturbances. Specifically, we propose exploiting the single agent update nature of the multiplexed approach, and fix the update sequence to enable input move-blocking and increased discretisation rates. This permits a higher rate of individual policy update to be achieved, whilst incurring no additional computational cost in the corresponding optimal control problems to be solved. A disturbance feedback policy is included between updates to facilitate finding feasible solutions. The new formulation inherits the property of rapid response to disturbances from multiplexing the control and numerical results show that fixing the update sequence does not incur any loss in performance. © 2011 IFAC.

ℓasso MPC: Smart regulation of over-actuated systems

In this paper, a novel MPC strategy is proposed, and referred to as asso MPC. The new paradigm features an 1-regularised least squares loss function, in which the control error variance competes with the sum of input channels magnitude (or slew rate) over the whole horizon length. This cost choice is motivated by the successful development of LASSO theory in signal processing and machine learning. In the latter fields, sum-of-norms regularisation have shown a strong capability to provide robust and sparse solutions for system identification and feature selection. In this paper, a discrete-time dual-mode asso MPC is formulated, and its stability is proven by application of standard MPC arguments. The controller is then tested for the problem of ship course keeping and roll reduction with rudder and fins, in a directional stochastic sea. Simulations show the asso MPC to inherit positive features from its corresponding regressor: extreme reduction of decision variables' magnitude, namely, actuators' magnitude (or variations), with a finite energy error, being particularly promising for over-actuated systems. © 2012 AACC American Automatic Control Council).

Stabilising terminal cost and terminal controller for ℓasso- MPC: Enhanced optimality and region of attraction

In recent literature, ℓ1-regularised MPC, or ℓasso-MPC, has been recommended for control tasks involving complex requirements on the control signals, for instance, the simultaneous solution of regulation and sharp control allocation for redundantly-actuated systems. This is due to the implicit thresholding ability of LASSO regression. In this paper, a stabilising terminal cost featuring a mixed ℓ1/ℓ2 2 penalty is presented. Then, a candidate terminal controller is computed, with the aim of enlarging the region of attraction. © 2013 EUCA.

The changing face and role of CACSD

Computer Aided Control Engineering involves three parallel streams: Simulation and modelling, Control system design (off-line), and Controller implementation. In industry the bottleneck problem has always been modelling, and this remains the case - that is where control (and other) engineers put most of their technical effort. Although great advances in software tools have been made, the cost of modelling remains very high - too high for some sectors. Object-oriented modelling, enabling truly re-usable models, seems to be the key enabling technology here. Software tools to support control systems design have two aspects to them: aiding and managing the work-flow in particular projects (whether of a single engineer or of a team), and provision of numerical algorithms to support control-theoretic and systems-theoretic analysis and design. The numerical problems associated with linear systems have been largely overcome, so that most problems can be tackled routinely without difficulty - though problems remain with (some) systems of extremely large dimensions. Recent emphasis on control of hybrid and/or constrained systems is leading to the emerging importance of geometric algorithms (ellipsoidal approximation, polytope projection, etc). Constantly increasing computational power is leading to renewed interest in design by optimisation, an example of which is MPC. The explosion of embedded control systems has highlighted the importance of autocode generation, directly from modelling/simulation products to target processors. This is the 'new kid on the block', and again much of the focus of commercial tools is on this part of the control engineer's job. Here the control engineer can no longer ignore computer science (at least, for the time being). © 2006 IEEE.

The changing face and role of CACSD

Computer Aided Control Engineering involves three parallel streams: Simulation and modelling, Control system design (off-line), and Controller implementation. In industry the bottleneck problem has always been modelling, and this remains the case - that is where control (and other) engineers put most of their technical effort. Although great advances in software tools have been made, the cost of modelling remains very high - too high for some sectors. Object-oriented modelling, enabling truly re-usable models, seems to be the key enabling technology here. Software tools to support control systems design have two aspects to them: aiding and managing the work-flow in particular projects (whether of a single engineer or of a team), and provision of numerical algorithms to support control-theoretic and systems-theoretic analysis and design. The numerical problems associated with linear systems have been largely overcome, so that most problems can be tackled routinely without difficulty - though problems remain with (some) systems of extremely large dimensions. Recent emphasis on control of hybrid and/or constrained systems is leading to the emerging importance of geometric algorithms (ellipsoidal approximation, polytope projection, etc). Constantly increasing computational power is leading to renewed interest in design by optimisation, an example of which is MPC. The explosion of embedded control systems has highlighted the importance of autocode generation, directly from modelling/simulation products to target processors. This is the 'new kid on the block', and again much of the focus of commercial tools is on this part of the control engineer's job. Here the control engineer can no longer ignore computer science (at least, for the time being). ©2006 IEEE.

Surface excavation with model predictive control

This paper describes the application of variable-horizon model predictive control to trajectory generation in surface excavation. A nonlinear dynamic model of a surface mining machine digging in oil sand is developed as a test platform. This model is then stabilised with an inner-loop controller before being linearised to generate a prediction model. The linear model is used to design a predictive controller for trajectory generation. A variable horizon formulation is augmented with extra terms in the cost function to allow more control over digging, whilst still preserving the guarantee of finite-time completion. Simulations show the generation of realistic trajectories, motivating new applications of variable horizon MPC for autonomy that go beyond the realm of vehicle path planning. ©2010 IEEE.