Fixed-point implementation of a proximal Newton method for embedded model predictive control (I)

Extending the success of model predictive control (MPC) technologies in embedded applications heavily depends on the capability of improving quadratic programming (QP) solvers. Improvements can be done in two directions: better algorithms that reduce the number of arithmetic operations required to compute a solution, and more efficient architectures in terms of speed, power consumption, memory occupancy and cost. This paper proposes a fixed point implementation of a proximal Newton method to solve optimization problems arising in input-constrained MPC. The main advantages of the algorithm are its fast asymptotic convergence rate and its relatively low computational cost per iteration since it the solution of a small linear system is required. A detailed analysis on the effects of quantization errors is presented, showing the robustness of the algorithm with respect to finite-precision computations. A hardware implementation with specific optimizations to minimize computation times and memory footprint is also described, demonstrating the viability of low-cost, low-power controllers for high-bandwidth MPC applications. The algorithm is shown to be very effective for embedded MPC applications through a number of simulation experiments

A new algorithm for solving convex parametric quadratic programs based on graphical derivatives of solution mappings

In this paper we derive formulas for computing graphical derivatives of the (possibly multivalued) solution mapping for convex parametric quadratic programs. Parametric programming has recently received much attention in the control community, however most algorithms are based on the restrictive assumption that the so called critical regions of the solution form a polyhedral subdivision, i.e. the intersection of two critical regions is either empty or a face of both regions. Based on the theoretical results of this paper, we relax this assumption and show how we can efficiently compute all adjacent full dimensional critical regions along a facet of an already discovered critical region. Coupling the proposed approach with the graph traversal paradigm, we obtain very efficient algorithms for the solution of parametric convex quadratic program

Hierarchical control of complex manufacturing processes

The need for changing the control objective during the process has been reported in many systems in manufacturing, robotics, etc. However, not many works have been devoted to systematically investigating the proper strategies for these types of problems. In this dissertation, two approaches to such problems have been suggested for fast varying systems. The first approach, addresses problems where some of the objectives are statically related to the states of the systems. Hierarchical Optimal Control was proposed to simplify the nonlinearity caused by adding the statically related objectives into control problem. The proposed method was implemented for contour-position control of motion systems as well as force-position control of end milling processes. It was shown for a motion control system, when contour tracking is important, the controller can reduce the contour error even when the axial control signals are saturating. Also, for end milling processes it was shown that during machining sharp edges where, excessive cutting forces can cause tool breakage, by using the proposed controller, force can be bounded without sacrificing the position tracking performance. The second approach that was proposed (Hierarchical Model Predictive Control), addressed the problems where all the objectives are dynamically related. In this method neural network approximation methods were used to convert a nonlinear optimization problem into an explicit form which is feasible for real time implementation. This method was implemented for force-velocity control of ram based freeform extrusion fabrication of ceramics. Excellent extrusion results were achieved with the proposed method showing excellent performance for different changes in control objective during the process --Abstract, page iv

Advanced multiparametric optimization and control studies for anaesthesia

Anaesthesia is a reversible pharmacological state of the patient where hypnosis, analgesia and muscle relaxation are guaranteed and maintained throughout the surgery. Analgesics block the sensation of pain; hypnotics produce unconsciousness, while muscle relaxants prevent unwanted movement of muscle tone. Controlling the depth of anaesthesia is a very challenging task, as one has to deal with nonlinearity, inter- and intra-patient variability, multivariable characteristics, variable time delays, dynamics dependent on the hypnotic agent, model analysis variability, agent and stability issues. The modelling and automatic control of anaesthesia is believed to (i) benefit the safety of the patient undergoing surgery as side-effects may be reduced by optimizing the drug infusion rates, and (ii) support anaesthetists during critical situations by automating the drug delivery systems. In this work we have developed several advanced explicit/multi-parametric model predictive (mp-MPC) control strategies for the control of depth of anaesthesia. State estimation techniques are developed and used simultaneously with mp-MPC strategies to estimate the state of each individual patient, in an attempt to overcome the challenges of inter- and intra- patient variability, and deal with possible unmeasurable noisy outputs. Strategies to deal with the nonlinearity have been also developed including local linearization, exact linearization as well as a piece-wise linearization of the Hill curve leading to a hybrid formulation of the patient model and thereby the development of multiparametric hybrid model predictive control methodology. To deal with the inter- and intra- patient variability, as well as the noise on the process output, several robust techniques and a multiparametric moving horizon estimation technique have been design and implemented. All the studies described in the thesis are performed on clinical data for a set of 12 patients who underwent general anaesthesia.Open Acces