Toward Co-Design Theory of Plant and Adaptive Control with Aerospace Applications

This paper introduces a new approach to handling uncertainties in a system obtained through a control co-design (CCD) technique, where the plant and control parameters are optimized jointly. Instead of using robust or stochastic optimization to address these uncertainties, we integrate an adaptive controller into the CCD problem formulation. This controller can account for unknown system dynamics and failures. However, this formulation appears to counter the core principle of adaptive control theory, which provides controllability without explicit knowledge of plant parameters. We argue that if part of the plant can be modified or optimized, which is often true in engineering applications, the system can better adapt to unknown dynamics under certain constraints, such as actuator saturation. We mathematically formulate the CCD problem as a general optimal control problem, where the control variables include static plant parameters and time-varying adaptation rates for control gains, derived using Lyapunov theory. The corresponding optimality conditions are obtained via Pontryagin’s principle. To make the problem tractable, we consider the adaptation rates to be time-invariant, reducing the formulation to a parametric optimization problem. An aerospace example involving helicopter pitch dynamics and control during hover, subject to a longitudinal cyclic position constraint, is provided to demonstrate the effectiveness of our approach.