Control of Constrained Dynamical Systems with Performance Guarantees: With Application to Vehicle motion Control
Doktorsavhandling, 2021

In control engineering, models of the system are commonly used for controller design. A standard control design problem consists of steering the given system output (or states) towards a predefined reference. Such a problem can be solved by employing feedback control strategies. By utilizing the knowledge of the model, these strategies compute the control inputs that shrink the error between the system outputs and their desired references over time. Usually, the control inputs must be computed such that the system output signals are kept in a desired region, possibly due to design or safety requirements. Also, the input signals should be within the physical limits of the actuators. Depending on the constraints, their violation might result in unacceptable system failures (e.g. deadly injury in the worst case). Thus, in safety-critical applications, a controller must be robust towards the modelling uncertainties and provide a priori guarantees for constraint satisfaction.

A fundamental tool in constrained control application is the robust control invariant sets (RCI). For a controlled dynamical system, if initial states belong to RCI set, control inputs always exist that keep the future state trajectories restricted within the set. Hence, RCI sets can characterize a system that never violates constraints. These sets are the primary ingredient in the synthesis of the well-known constraint control strategies like model predictive control (MPC) and interpolation-based controller (IBC). Consequently, a large body of research has been devoted to the computation of these sets. In the thesis, we will focus on the computation of RCI sets and the method to generate control inputs that keep the system trajectories within RCI set. We specifically focus on the systems which have time-varying dynamics and polytopic constraints. Depending upon the nature of the time-varying element in the system description (i.e., if they are observable or not), we propose different sets of algorithms.

The first group of algorithms apply to the system with time-varying, bounded uncertainties. To systematically handle the uncertainties and reduce conservatism, we exploit various tools from the robust control literature to derive novel conditions for invariance. The obtained conditions are then combined with a newly developed method for volume maximization and minimization in a convex optimization problem to compute desirably large and small RCI sets. In addition to ensuring invariance, it is also possible to guarantee desired closed-loop performance within the RCI set. Furthermore, developed algorithms can generate RCI sets with a predefined number of hyper-planes. This feature allows us to adjust the computational complexity of MPC and IBC controller when the sets are utilized in controller synthesis. Using numerical examples, we show that the proposed algorithms can outperform (volume-wise) many state-of-the-art methods when computing RCI sets.

In the other case, we assume the time-varying parameters in system description to be observable. The developed algorithm has many similar characteristics as the earlier case, but now to utilize the parameter information, the control law and the RCI set are allowed to be parameter-dependent. We have numerically shown that the presented algorithm can generate invariant sets which are larger than the maximal RCI sets computed without exploiting parameter information.

Lastly, we demonstrate how we can utilize some of these algorithms to construct a computationally efficient IBC controller for the vehicle motion control. The devised IBC controller guarantees to meet safety requirements mentioned in ISO 26262 and the ride comfort requirement by design.

Linear fractional transformation

Robust control

Linear parameter varying system

Invariant set

Semi-definite program

Linear matrix inequalities

Opponent: Prof. Mircea Lazar, Eindhoven University of Technology, The Netherlands


Ankit Gupta

Chalmers, Elektroteknik, System- och reglerteknik

Computation of Robust Control Invariant Sets with Predefined Complexity for Uncertain Systems

International Journal of Robust and Nonlinear Control,; Vol. 31(2021)p. 1674-1688

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Paper i proceeding

A. Gupta, M. Mejari, P. Falcone, D. Piga, Computation of Parameter Dependent Invariant Sets for LPV Systems with Guaranteed Performance

In model-based control, the mathematical model of the system is used to construct feedback controllers. Therefore, the model should capture the most relevant system dynamics. However, this may not be the case in practice. That is uncertainties unavoidably become part of the model, and hence robust controllers need to be designed. Furthermore, these systems usually operate under constraints due to physical limitation, or artificially imposed for safety and performance. As a result, the obtained models are uncertain and constrained, for which designing a controller could be a challenging task.

The main objective of the thesis is to propose control methods, with performance guarantees, for constrained uncertain system. To meet the objectives, we present algorithms that compute a stabilizing controller, along with a set of states where the system is guaranteed to satisfy constraints. In the control theory, these sets are well-known as invariant sets and widely used in safety-critical applications to enforce the controllers' safety.

Further, we demonstrate how we can utilize these algorithms to construct a controller for vehicle motion control application. This is a relevant application to show the thesis contribution. Because for high-level autonomous vehicles, the controller has to guarantee the satisfaction of recently introduced Automotive Safety Integrity Level (ASIL) requirements mentioned in ISO 26262. For such an application, we propose a constrained control strategy which ensures safety by design.


Hållbar utveckling




Elektroteknik och elektronik



Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 4904




Opponent: Prof. Mircea Lazar, Eindhoven University of Technology, The Netherlands

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