Program

Romeo Ortega

PID Passivity-based Control of Nonlinear Systems with Applications

Motivated by current practice, in this talk we explore the possi bility of applying the industry-standard PID controllers to regulate the behavior of nonlinear systems. As is well-known, PID controllers are highly successful when the main control objective is to drive a given output signal to a constant value. PIDs, however, have two main drawbacks, first, the task of tuning the gains is far from obvious when the systems operating region is large; second, in some practical applications the control objective cannot be captured by the behaviour of output signals. We show that, for a wide class of physical systems, these two difficulties can be overcome exploiting the property of passivity of the system. Passivity is a fundamental property of dynamical systems, which in the case of physical systems captures the universal feature of energy conservation. It is well-known that PID controllers are passive systems—for all positive PID gains—and that the feedback interconnection of two passive systems is stable. Therefore, wrapping the PID around a passive output trivialises the gain tuning task. Clearly, the first step in the design is to identify all passive outputs of the system. It turns out that this task is achievable for a large class of physical systems described by port-Hamiltonian models. In many applications the desired values for the outputs are different from zero, whence the PID is wrapped around the error signal. In this case, it is necessary to investigate whether the system is passive with respect to this error signal—a property called shifted passivity, which is also studied in the talk. If the control objective is to stabilize (in the Lyapunov sense) a constant equilibrium it is necessary to build a Lyapunov function. In the talk we identify—via some easily verifiable integrability conditions—a class of systems for which this more ambitious objective is achieved. Many mechanical and electrical systems practical applications where PID-PBC is successful are studied in the talk. Among them we cite: robots, power systems, power electronic converters, micro-electromechanical devices, levitated systems, fuel-cells systems and motors. In view of this wide range of applications, besides control theorists, the talk may be of interest to practitioners working on these fields and to people from industry.

Gustavo Artur de Andrade

Backstepping Methods for Analysis, Control, and Observation of Thermoacoustic Rijke Tube Dynamics

Thermoacoustic oscillations in Rijke tubes serve as a canonical prototype for the instabilities that arise in more complex thermoacoustic systems, where heat release couples with acoustic waves to produce self-sustained oscillations. In this presentation, I discuss recent advances in the analysis, control, and estimation of these oscillations using backstepping techniques for first-order hyperbolic PDEs. The first part addresses the stabilization of a linearized ODE–PDE Rijke tube model, showing how an explicit backstepping transformation enables the construction of a boundary controller that achieves exponential suppression of the acoustic energy. Motivated by experimental observations, the second part focuses on state estimation and introduces a backstepping-based boundary observer capable of reconstructing both the acoustic field and the coupling variables, with validation using data from a laboratory Rijke tube setup. Overall, the results highlight how backstepping offers a unified and constructive framework for understanding, stabilizing, and observing thermoacoustic PDE models, bridging rigorous infinite-dimensional control theory with experimental thermoacoustic systems.

Florian Dörfler

Data-Enabled Predictive Control (DeePC)

We consider the problem of optimal and constrained predictive control for unknown systems. We adopt a behavioral systems perspective and characterize the subspace of trajectories of a linear system by means of raw data assembled in a matrix. A data-enabled predictive control (DeePC) algorithm is presented that leverages this data-driven representation to compute optimal and safe control trajectories. We show that, in the case of deterministic linear time-invariant systems, the DeePC algorithm is equivalent to the widely adopted Model Predictive Control (MPC), but it often outperforms subsequent system identification and model-based control. To robustify the method against noise, nonlinearities, and distributional uncertainty, we propose salient regularizations to the DeePC algorithm. Last we present some recent bottom-up extensions towards a Gaussian behavioral system theory, and show how to leverage mean and variance of the trajectory space to improve the closed-loop performance in a stochastic context. We illustrate our results with nonlinear and noisy simulations and experiments from aerial robotics, power electronics, and power systems. 

Antonio Estrada

Sliding Mode Control: Study Cases

Sliding mode control has been established as a robust control technique rendering good performance despite the presence of uncertainties. Theoretically insensitive to matched perturbations, several schemes have appear in order to tackle the unmatched perturbation problem. The presentation describes the usage of sliding mode control in different dynamical systems which stems from real applications such as aircrafts, laser cladding manufacturing systems and refrigeration systems. The study cases are related to theoretical problems such as strict-feedback/block control problem, multiplicative disturbances, among others.

Tamer Başar

Inducement of Behavior via Soft Policies: A Mathematical Theory

Terms like inducement, incentivization, persuasion, and to some extent enticement, are used in our daily lives to describe situations where one individual (decision maker, or entity) acts in a way to influence the decision-making process of another individual or individuals, where the outcome could benefit all involved or only the one who has initiated the process. Such influence could be exerted in two different ways (though variations do exist): via a direct input by the influencer into the utility or reward (or loss) of the receiving party, or by controlling (and possibly crafting) the information flow to the latter toward shaping beliefs at the receiving end (as in spread of disinformation). Both scenarios (and those that fall in between) could be analyzed within a dynamic Stackelberg game-theoretic framework with a precise notion of equilibrium, which this talk will address. The focus will naturally be on soft inducement (incentivization, persuasion) policies, rather than hard enforcement (such as threat) ones which are not that interesting (at least mathematically) or practical. The talk will introduce some explicit models that lead to appealing such policies and discuss a diverse set of mathematical machinery used to derive them. The talk will also include discussions on the impact of various factors, such as population size, placement of intermediaries, uncertainty in modeling, and disparate probabilistic outlooks by the decision makers, on the resulting equilibria, and identify several challenges that lie ahead.

Miroslav Krstic

Nonholonomic Stabilization: Fixed-Time and Inverse-Optimal Adaptive

For parking nonholonomic mobile robots, globally uniformly Lagrange asymptotically stabilizing (GULAS) feedback laws are presented, which don’t contradict Brockett’s condition. Strict CLFs are also constructed, which are then employed to, additionally, design LgV-type feedback laws. Besides the inverse optimality, due to the drifless nature of the unicycle model, the LgV feedbacks impart not only [1/2, infinity) but (0,infinity) gain margins with respect to uncertain input coefficients. Then, for unknown input coefficients, inverse optimal ADAPTIVE feedback laws are designed, which both reduce the peak control efforts (the longitudinal and angular velocities) and are optimal over the infinite horizon. Their cost functionals not only penalize the control effort and the unicycle’s three states, but also the parameter estimation errors - over the entire horizon, not only in the asymptotic limit. Finally, for parking in user-desired time, two feedback laws are designed: (1) a time-varying feedback, with gains that are singular at terminal time but keep the controls bounded, and (2) a static homogeneous feedback, which is nonsmooth at the target values of position and heading. 

Coffee-Break: 16:00 - 16:30

Mario A. Rotea

Extremum Seeking Flow Control in Wind Farms

Wind energy is one of the leading sources of renewable electricity worldwide. Many countries aim to expand wind power capacity and integrate it more deeply into electric grids. Achieving this goal requires reducing the overall cost of wind energy. Advanced control systems can help by increasing energy production and lowering operation and maintenance costs. One promising approach is wake steering, where the yaw angles of upstream turbines are adjusted to redirect their wakes away from downstream turbines. This increases wind speed at the downstream turbines and boosts total power output for the wind farm. In this talk, we present the use of extremum seeking control to optimize yaw angles for wake steering and maximize wind farm power. Experimental results from scaled wind turbines in the UTD Atmospheric Boundary Layer wind tunnel demonstrate the benefits and potential limitations of this method.

Martin Guay

Data-Driven Control of Unknown Nonlinear Systems using Extremum Seeking

The complexity of system dynamics can often be an obstacle in the development of reliable dynamical models. In classical control engineering methodologies, the knowledge of the system’s dynamics has always been a key element in the design, testing and implementation of control systems. Since the development of reliable dynamical models is often restrictively onerous and fraught with technical and experimental difficulties, the access of high-quality dynamical models is often limited. The last ten years has seen a tremendous amount of research activity on the development of model free control techniques. One leading technique is extremum-seeking control (ESC). This technique has been applied extensively in many application areas such as biomedical engineering, aerospace engineering, automotive, biotechnology and process control. In this presentation, we seek to review some of the new developments on the generalization of extremum seeking control as a data-driven controller design technique. It is shown how one can apply this technique to design reliable control systems that require only limited knowledge of the system dynamics. Several applications are presented to demonstrate the versatility of this technique. 

Emilia Fridman

Constructive Methods for Averaging-Based Control

An efficient method for stability of systems with rapidly oscillating coefficients is averaging: the system is stable for small enough values of the parameter provided the averaged system is stable. All the existing methods for averaging are qualitative without giving quantitative bounds on the small parameter. In this talk I will present new constructive approaches to averaging that are based on time-delay and delay-free transformations and special model presentations. The results will be applied to stabilization of unstable systems by fast switching, power systems and Brocket problem (static output-feedback by using time-varying gains) and to extremum seeking (a powerful real-time optimization method without requesting a knowledge of system model). These are joint results with my recent post-docs Yang Zhu (Zhejiang University), Jin Zhang (Shanghai University) and Xuefei Yang (Harbin Institute of Technology) and former PhD student Rami Katz (Trento University) .