A major goal in the control of complex mechanical systems such as advanced aircraft, spacecraft, and power plants is to achieve high performance with increased reliability, availability, component durability, and maintainability. The current state-of-the-art of control systems synthesis focuses on improving performance and diagnostic capabilities under constraints that often do not adequately represent the dynamic properties of the materials. The reason is that the traditional design is based upon the assumption of conventional materials with invariant characteristics. In view of high performance requirements and availability of improved materials, the lack of appropriate knowledge about the properties of these materials will lead to either less than achievable performance due to overly conservative design, or over-straining of the structure leading to unexpected failures and drastic reduction of the service life. The key idea of the research reported in this paper is that a significant improvement in service life can be achieved by a small reduction in the system dynamic performance. This requires augmentation of the current system-theoretic techniques for synthesis of decision and control laws with governing equations and inequality constraints that would model the properties of the materials for the purpose of damage representation and failure prognosis. The major challenge in this research is to characterize the damage generation process in a continuous-time setting, and then utilize this information for synthesizing algorithms of robust control, diagnostics, and risk assessment in complex mechanical systems. Damage mitigation for control of mechanical systems is reported in the two-part paper. The concept of damage mitigation is introduced and a continuous-time model of fatigue damage dynamics is formulated in this paper which is the first part. The second part which is a companion paper presents the synthesis of the open-loop control policy and the results of simulation experiments for transient operations of a reusable rocket engine.

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