Discrete-Time Constrained PI-like Output Feedback Tracking

This repository contains the numerical implementation and simulation scripts for the methodology proposed in:

"Discrete-Time Constrained PI-like Output Feedback Tracking Controllers - a Robust Positive Invariance and Bilinear Programming Approach" > Geovana F. Dos Santos, Jackson Ernesto, Eugênio B. Castelan, and Walter Lucia > EasyChair Preprint FF2k

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📖 Overview

This project provides an optimization-based design for a PI-like output feedback tracking controller. It ensures offset-free tracking for linear discrete-time systems while strictly respecting state and input constraints.

Key Technical Features:

• Internal Model Principle: Integrated to guarantee zero steady-state error for set-point references.

• Constraint Handling: Uses polyhedral sets for both states ($x \in \mathcal{X}$) and inputs ($u \in \mathcal{U}$).

• Bilinear Programming: Formulates the controller gain and invariant set design as a single optimization problem.

• Robust Positive Invariance (RPI): Guarantees that if the system starts within the designed set, it remains there for all future time steps.

🛠 Software Requirements

The implementation uses the AMPL (A Mathematical Programming Language) environment with high-performance nonlinear solvers:

• Modeling: AMPL

• [cite_start]Solver: Artelys KNITRO (specifically configured for multi-start global optimization)[cite: 84, 85].

• Alternative Solvers: The code is compatible with other AMPL-supported solvers like IPOPT or SNOPT.

🚀 Repository Structure & Usage

📂 File Descriptions

• ex.mod: The mathematical model containing the objective function and constraints.

• ex.dat: Numerical parameters for the Two-Tank System benchmark ($T_s = 1s$)[cite: 1, 10].

• ex.run: Execution script that configures the solver and exports results to .out files[cite: 84, 87].

📋 Running the Design

1. Ensure AMPL and Knitro are installed and in your system path.

2. Run the command:

   ampl ex.run