[Paper Review] Optimal Control Design with Limited Model Information y

Farhad Farokhi, Karl Henrik Johansson|arXiv (Cornell University)|Dec 16, 2011

Advanced Control Systems Optimization30 references2 citations

TL;DR

This paper proposes a family of optimal control design methods that use limited model information—specifically local plant model data and global interconnection structure—via a design graph to achieve structured static state-feedback control. The key contribution is the derivation of optimal control strategies under separable quadratic cost, with performance quantified via competitive ratio and domination metrics, revealing a trade-off between model information and closed-loop performance.

ABSTRACT

We introduce the family of limited model information control design methods, which construct controllers by accessing the plant’s model in a constrained way, according to a given design graph. We investigate the achievable closed-loop performance of discrete-time linear time-invariant plants under a separable quadratic cost performance measure with structured static state-feedback controllers. We nd the optimal control design strategy (in terms of the competitive ratio and domination metrics) when the control designer has access to the local model information and the global interconnection structure of the plant-to-be-controlled. At last, we study the trade-o between the amount of model information exploited by a control design method and the best closed-loop performance (in terms of the competitive ratio) of controllers it can produce.

Motivation & Objective

• To develop control design methods that operate under constrained access to plant model information while leveraging global interconnection structure.
• To determine the optimal control strategy for discrete-time linear time-invariant plants under a separable quadratic cost function.
• To quantify the best achievable closed-loop performance when only partial model information is available.
• To analyze the trade-off between the amount of model information used and the resulting controller performance.
• To establish performance metrics such as competitive ratio and domination to evaluate controller optimality.

Proposed method

• The method constructs controllers based on a design graph that encodes which model parameters are accessible to the designer.
• It employs structured static state-feedback control laws where controller gains are constrained by the sparsity pattern of the design graph.
• The performance is evaluated using a separable quadratic cost function over the closed-loop system.
• Optimal control design is formulated as a constrained optimization problem to minimize the competitive ratio relative to full-information optimal control.
• The approach leverages the global interconnection structure of the plant to guide controller synthesis despite limited local model access.
• Theoretical bounds on performance are derived using domination metrics and competitive ratio analysis.

Experimental results

Research questions

• RQ1 What is the optimal control design strategy when only local model information and global interconnection structure are available?
• RQ2 How does the amount of model information affect the best possible closed-loop performance in terms of competitive ratio?
• RQ3 Can a structured static state-feedback controller achieve optimal performance under limited model access?
• RQ4 What performance metrics (e.g., competitive ratio, domination) are most suitable for evaluating limited-information control designs?
• RQ5 How does the design graph influence the trade-off between model information and controller performance?

Key findings

• The optimal control design strategy under limited model information is derived using competitive ratio and domination metrics, providing a performance benchmark.
• The best achievable closed-loop performance is bounded by the amount of model information accessible through the design graph.
• A clear trade-off is established between the quantity of model information used and the resulting competitive ratio of the controller.
• Controllers designed with only local model data and global structure information can achieve performance close to full-information optimal control under specific conditions.
• The design graph plays a critical role in determining which controller structures are feasible and optimal under information constraints.
• The competitive ratio serves as a robust performance metric for comparing limited-information control strategies.