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There are two main approaches to control gain synthesis an internal model-based distributed dynamic state feedback control law for the linear cooperative output regulation problem: (i) agent-wise local design methods, (ii) global design methods. Agent-wise local design methods to synthesize distributed control gains focus on the individual dynamics of each agent to guarantee the overall stability of the system. They are powerful tools due to their scalability. However, the agent-wise local design methods are incapable of maximizing the overall system performance through, for example, decay rate assignment. On the other hand, design methods, which are predicated on a global condition, lead to nonconvex optimization problems. We present a convex formulation of this global design problem based on a structured Lyapunov inequality. Then, the existence of solutions to the structured Lyapunov inequality is investigated. Specifically, we analytically show that the solutions exist for the systems satisfying the agent-wise local sufficient condition. Finally, we compare the proposed method with the agent-wise local design method through numerical examples in terms of conservatism, performance maximization, graph dependency, and scalability.
Systems with dynamics evolving in distinct slow and fast timescales include aircraft (Khalil & Chen, 1990), robotic manipulators, (Tavasoli, Eghtesad, & Jafarian, 2009), electrical power systems (Sauer, 2011), chemical reactions (Mélykúti, Hespanha, & Khammash, 2014), production planning in manufacturing (Soner, 1993), and so on. The Geometric Singular Perturbation theory (Fenichel, 1979) is a powerful control law development tool for multiple-timescale systems because it provides physical insight into the evolution of the states in more than one timescale. The behaviour of the full-order system can be approximated by the slow subsystem, provided that the fast states can be stabilised on an equilibrium manifold. The fast subsystem describes how the fast states evolve from their initial conditions to their equilibrium trajectory or the manifold. This presentation develops two nonlinear, multiple-time-scale, output feedback tracking controllers for a class of nonlinear, nonstandard systems with slow and fast states, slow and fast actuators, and model uncertainties. The class of systems is motivated by aircraft with uncertain inertias, control derivatives, engine time-constant, and without direct measurement of angle-of-attack and sideslip angle. One controller achieves the control objective of slow state tracking, while the other does simultaneous slow and fast state tracking. Each controller is synthesized using time-scale separation, lower-order reduced subsystems, and estimates of unknown parameters and unmeasured states. The estimates are updated dynamically, using an online parameter estimator and a nonlinear observer. The update laws are so chosen that errors remain ultimately bounded for the full-order system. The controllers are simulated on a six-degree-of-freedom, high-performance aircraft model commanded to perform a demanding, combined longitudinal and lateral/directional maneuver. Even though two important aerodynamic angles are not measured, tracking is adequate and as good as a previously developed full-state feedback controller handling similar parametric uncertainties. Additionally, even though the two controllers in theory achieve two different control objectives, it is possible to choose either one of them for the same maneuver. Of the two new output feedback controllers, the slow state tracker accomplishes the maneuver with less control effort, while the simultaneous slow and fast state tracker does so with a smaller number of gains to tune.
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In cyber-physical systems, safety and availability are of utmost importance. To satisfy requirements on safety and availability, suitable supervisory controllers need to be employed. Supervisory control theory provides a foundation on which a model-based engineering method has been developed, providing guarantees on the correctness of resulting supervisory controllers with respect to the defined requirements. In this lecture, an overview will be given of the recent research projects at Eindhoven University of Technology aiming at the development of extensions to this method, and of supporting tools, giving rise to an integrated approach to the design of supervisory controllers for complex real-life systems. This includes a mathematically underpinned, straightforward and error-free path to implementation of the designed controllers. The research projects are related to the partnership with Rijkswaterstaat which is a part of the Dutch Ministry of Infrastructure and Water Management.
This talk presents recent results in nonlinear observer design and their applications in motion estimation problems ranging from wearable sensors to bicycles. First, a new observer design technique that integrates the classical high-gain observer with a novel LPV/LMI observer to provide significant advantages compared to both methods is presented. Second, the challenges in designing observers for nonlinear systems which are non-monotonic are discussed. Non-monotonic systems are commonly encountered, but popular observer design methods fail to yield feasible solutions for such systems. Hybrid observers with switched gains enable existing observer design methods to be utilized for these systems. Following the analytical observer results, some of their applications in motion estimation are presented, including a wearable device for Parkinson’s disease patients, a smart bicycle that automatically tracks the trajectories of nearby vehicles on the road to protect itself, and smart agricultural/construction vehicles that utilize inexpensive sensors for end-effector position estimation. Each application is accompanied by a video of a prototype experimental demonstration. One of these applications has been successfully commercialized through a start-up company which expects to sell over 5,000 sensor boards this year.
Mechanical motion generation and vibration suppression is fundamental to modern machines and emerging innovations. Abilities to learn and compensate for complex mechanical system and disturbance dynamics are key to synthesizing adequate control actions to achieve precision motions. Using application case studies to motivate challenges and demonstrate implementation results, I will present control methods for addressing narrowband (repetitive control, iterative learning control) and broadband (adaptive control) motions and disturbances. I will attempt to convey a common theme, controller syntheses stemming from ideas of system dynamic inversions and utilizing solutions of optimal model matching problems.
Genetic circuits control every aspect of life and thus the ability to engineer them de-novo opens exciting possibilities, from revolutionary drugs and green energy to bugs that recognize and kill cancer cells. Just like in mechanical, electrical, and hydraulic systems, the problem of loading, or back-action, is encountered when engineering genetic circuits. These molecular loads can be severe to the point of completely destroying the intended function of a circuit. In this talk, I will review a systems theoretic modeling formalism, grounded on the concept of retroactivity, that captures molecular loads in a way that makes the loading problem amenable of a solution. I will, in particular, focus on two types of loading: inter-module loads and loads to cellular resources that feed the modules. I will show experimentally validated models of loading effects on the emergent dynamics of a system and nonlinear control techniques that we have developed and implemented to mitigate these effects.
