Showing papers by "Wpmh Maurice Heemels published in 2019"

Practical Stabilization of Switched Affine Systems With Dwell-Time Guarantees

Abstract: Using a hybrid systems approach, we address the practical stabilization of operating points for switched affine systems, ensuring a minimum dwell time and an admissible chattering around the operating point. Two different solutions are shown to induce uniform dwell time, based on time or space regularization. The proposed solutions provide useful tuning knobs to separately adjust the switching frequency during transients and at the steady state. The strengths of the method are illustrated by simulating a boost converter.

Periodic Event-Triggered Sampling and Dual-Rate Control for a Wireless Networked Control System With Applications to UAVs

Abstract: In this paper, periodic event-triggered sampling and dual-rate control techniques are integrated in a wireless networked control system (WNCS), where time-varying network-induced delays and packet disorder are present. Compared to the conventional time-triggered sampling paradigm, the control solution is able to considerably reduce network utilization (number of transmissions), while retaining a satisfactory control performance. Stability for the proposed WNCS is ensured using linear matrix inequalities. Simulation results show the main benefits of the control approach, which are experimentally validated by means of an unmanned-aerial-vehicle-based test-bed platform.

Event-Triggered Quantized Control for Input-to-State Stabilization of Linear Systems With Distributed Output Sensors

Abstract: We study output-based stabilization of linear time-invariant systems affected by unknown external disturbances. The plant outputs are measured by a collection of distributed sensors, which transmit their feedback information to the controller in an asynchronous fashion over different digital communication channels. Before transmission of measurements is possible quantization is needed, which is carried out by means of dynamic quantizers. To save valuable communication resources, the transmission instants of each sensor are determined by event-triggering mechanisms that only depend on locally available information. We propose a systematic methodology for the joint design of the (distributed) dynamic quantizers and the event-triggering mechanisms ensuring an input-to-state stability property of a size-adjustable set around the origin. Moreover, the proposed approach prevents the occurrence of Zeno behavior on the transmission instants and on the updates of the quantizer variable thereby guaranteeing that a finite number of data is transmitted within each finite time window. The tradeoff between transmissions and quantization is characterized in terms of the design parameters. The method is feasible for any stabilizable and detectable linear plant. The systematic design procedure and the effectiveness of the approach are illustrated on a numerical example.

Model predictive control for MR-HIFU-mediated, uniform hyperthermia

Abstract: Purpose: In local hyperthermia, precise temperature control throughout the entire target region is key for swift, safe, and effective treatment. In this article, we present a model predictive control (MPC) algorithm providing voxel-level temperature control in magnetic resonance-guided high intensity focused ultrasound (MR-HIFU) and assess the improvement in performance it provides over the current state of the art. Materials and methods: The influence of model detail on the prediction quality and runtime of the controller is evaluated and a tissue mimicking phantom is characterized using the resulting model. Next, potential problems arising from modeling errors are evaluated in silico and in the characterized phantom. Finally, the controller's performance is compared to the current state-of-the-art hyperthermia controller in side-by-side experiments. Results: Modeling diffusion by heat exchange between four neighboring voxels achieves high predictive performance and results in runtimes suited for real-time control. Erroneous model parameters deteriorate the MPC's performance. Using models derived from thermometry data acquired during low powered test sonications, however, high control performance is achieved. In a direct comparison with the state-of-the-art hyperthermia controller, the MPC produces smaller tracking errors and tighter temperature distributions, both in a homogeneous target and near a localized heat sink. Conclusion: Using thermal models deduced from low-powered test sonications, the proposed MPC algorithm provides good performance in phantoms. In direct comparison to the current state-of-the-art hyperthermia controller, MPC performs better due to the more finely tuned heating patterns and therefore constitutes an important step toward stable, uniform hyperthermia.

Extended Projected Dynamical Systems with Applications to Hybrid Integrator-Gain Systems

Abstract: The class of projected dynamical systems (PDS) has proven to be a powerful framework for modeling dynamical systems of which the trajectories are constrained to a set by means of projection. However, PDS fall short in modeling systems in which the constraint set does not satisfy certain regularity conditions and only part of the dynamics can be projected. This poses limitations in terms of the phenomena that can be described in this framework especially in the context of systems and control. Motivated by hybrid integrator-gain systems (HIGS), which are recently proposed control elements in the literature that aim at overcoming fundamental limitations of linear time-invariant feedback control, a new class of discontinuous dynamical systems referred to as extended projected dynamical systems (ePDS) is introduced in this paper. Extended projected dynamical systems include PDS as a special case and are well-defined for a wider variety of constraint sets as well as partial projections of the dynamics. In this paper, the ePDS framework is connected to the classical PDS literature and is subsequently used to provide a formal mathematical description of a HIGS-controlled system, which was lacking in the literature so far. Based on the latter result, HIGS-controlled systems are shown to be well-posed, in the sense of global existence of solutions.

Event-Triggered Consensus for Multi-Agent Systems with Guaranteed Robust Positive Minimum Inter-Event Times

Abstract: We study consensus seeking single-integrator multi-agent systems equipped with packet-based communication channels. As the communication bandwidth of such channels is typically limited, it is essential to consider control schemes that lead to the desired performance while not overusing the communication resources. For this purpose, we propose a distributed dynamic event-triggered control scheme that results in aperiodic information exchange between agents, asymptotic consensus, strictly positive lower bounds on the inter-event times (strong Zeno-freeness) and robustness to unknown, non-uniform, and time-varying transmission delays. The proposed framework is such that the local control laws and event-triggering mechanisms can be directly obtained from the number of connected agents and local tuning parameters. The proposed design framework is therefore applicable to large-scale multi-agent systems.

A System-Theoretic Approach to Construct a Banded Null Basis to Efficiently Solve MPC-Based QP Problems *

Abstract: The null-space method is able to reduce the number of decision variables in the on-line optimization carried out in model predictive control. This method relies on the construction of a basis for the null space of the equality constraints. This paper proposes a systematic approach based on system-theoretic insights to construct such a basis with a banded structure. This banded structure carries over to the resulting lower-dimensional QP and can be exploited to compute a solution more efficiently. Specifically, solvers that exploit this structure result in a computational complexity that scales linearly with the prediction horizon. In contrast to similar approaches in the literature, the proposed method can be applied to uncontrollable, though stabilizable, systems with multiple inputs. This method is particularly interesting when dealing with systems with large state dimension and long prediction horizons. Finally, the method is applied to a numerical example in combination with both the alternating direction method of multipliers and the accelerated dual gradient projection method to demonstrate its benefits.

Hybrid Integral Reset Control with Application to a Lens Motion System

Abstract: A hybrid integral controller with reset is proposed. This hybrid controller ensures improved low-frequency disturbance rejection properties under double integrator (PI2D) control without inducing the undesired increase of overshoot otherwise resulting from adding an extra linear integrator to a PID controller. The controller is applied to an optical lens motion system that requires PID control in one operating mode and PI2D control in the other, therewith motivating a hybrid integral control strategy. The reset element in the controller is included to improve transient performance. To guarantee closed-loop stability, a conditional (and partial) reset rule is introduced that restricts the input-output behavior of the dynamic reset element, i.e., the hybrid integrator with reset, to a bounded sector. As a result, stability can be guaranteed on the basis of a circle criterion-like argument and checked by (measured) frequency response data. Stability and performance of the hybrid integral control design with conditional (and partial) reset are investigated by application to a piezo-actuated lens system that is part of an industrial wafer scanner.

On the graphical stability of hybrid solutions with non-matching jump times: Extended Paper

Abstract: We investigate stability of a solution of a hybrid system in the sense that the graphs of solutions from nearby initial conditions remain close and tend towards the graph of the given solution. In this manner, a small continuous-time mismatch is allowed between the jump times of neighbouring solutions and the `peaking phenomenon' is avoided. We provide conditions such that this stability notion is implied by stability with respect to a specifically designed distance-like function. Hence, stability of solutions in the graphical sense can be analysed with existing Lyapunov techniques.

State-feedback event-holding control for nonlinear systems

Abstract: We propose a novel triggering policy to implement state-feedback controllers for nonlinear systems via packet-based communication networks. The idea is to generate transmissions between the plant and the controller only when a state-dependent rule has been satisfied for a given amount of time. We refer to this new paradigm as event-holding control, in which a clock variable is thus only running when a state-dependent criterion is verified. This is different from time-regularized event-triggered control, where the clock variable keeps running after each transmission instant until it is reset to zero at the moment a state-based condition is verified. We approach the problem of designing an event-holding controller via emulation. We first synthesize a state-feedback law, which stabilizes the closed-loop system in the absence of the communication network. We then design the event-holding triggering mechanism under a set of general assumptions. The results are applied to two case studies consisting of linear systems and a class of nonlinear systems controlled by backstepping. We also provide a numerical backstepping control example, which demonstrates that the event-holding behaviour can reduce the number of transmissions.