Contributions to the Output Feedback Controller Design for LPV Systems Subject to Amplitude Bounded Perturbations and with Constrained Control Input Variations

• Grant number: 24/10299-8
• Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil
• Start date: October 01, 2024
• End date: December 10, 2024
• Field of knowledge: Engineering - Electrical Engineering - Industrial Electronics, Electronic Systems and Controls
• Principal Investigator: Pedro Luis Dias Peres
• Grantee: Pedro Luis Dias Peres
• Visiting researcher: Eugenio de Bona Castelan Neto
• Visiting researcher institution: Universidade Federal de Santa Catarina (UFSC). Centro Tecnológico, Brazil
• Host Institution: Faculdade de Engenharia Elétrica e de Computação (FEEC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

The objective of the research is to develop methods for designing output feedback controllers for linear parameter-varying (LPV) systems. These systems are subject to persistent disturbances with limited amplitudes and have limits on the rate of variation of control inputs. The goal is to develop algebraic conditions to calculate feedback gains explicitly and to define local stability domains for the closed-loop system. These conditions will consider constraints in states and control, and the presence of persistent disturbances.The research will utilize the concepts of invariance and contractivity of convex sets associated with dynamical systems and optimization techniques. These will be used to determine feedback gains and obtain stability domains with appropriate sizes. Specifically, the Robust Positive Invariance (RPI) will be employed to ensure that the trajectories starting from a convex set in the state space of the system remain there and ultimately converge in finite time to a set around the origin, where they will remain ultimately bounded (UB). RPI sets can have a polyhedral form representing constraints and disturbance limits or the form obtained from level sets associated with Lyapunov functions dependent on variant parameters (FLDP).In the case of polyhedral RPI sets, the framework used by the Visitor allowed the development of output feedback design techniques for LPV systems based on the use of bilinear optimization. These optimization problems allow for solving the algebraic relations that describe the RPI and guarantee the admissibility of the whole regarding constraints and disturbances. Furthermore, the framework represents the system in an augmented space that allows modeling the increase in control variables as a virtual input, thus considering constraints on the control variation rate. However, these bilinear design techniques have a high computational cost but can be adapted for local stability analysis to reduce this cost.On the other hand, the Responsible has research related to the stabilization of different types of dynamic systems, including some that can be seen in the form of LPV, such as Takagi-Sugeno, uncertain, switched, and network control systems. The methodology uses conditions developed from FLDPs and optimization techniques based on linear matrix inequalities (LMIs). This allows the treatment of several problems related to robust control, including the use of output feedback and the presence of constraints and disturbances.In this context, the goal is to extend the framework described for polyhedral sets to determine RPI sets via FLDPs. This extension will use recent results that also allow obtaining feedback gains explicitly through an iterative approach based on LMIs. The potential impact of this research is significant, as it will enable a comparison of two approaches in terms of numerical efficiency, controller performance, and size of invariant regions. This will pave the way for the integration of the two techniques for design via LMIs and local stability analysis via bilinear optimization, thereby advancing the field of control systems and stability analysis. (AU)