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Motivated by uncertain parameters in nonlinear dynamic systems, we define a nonclassical optimal control problem where the cost functional is given by a Riemann-Stieltjes "functional of a functional." Using the properties of Riemann-Stieltjes sums, a minimum principle is generated from the limit of a semidiscretization. The optimal control minimizes a Riemann-Stieltjes integral of the Pontryagin Hamiltonian. The challenges associated with addressing the noncommutative operations of integration and minimization are addressed via cubature techniques leading to the concept of hyper-pseudospectral points. These ideas are then applied to address the practical uncertainties in control moment gyroscopes that drive an agile spacecraft. Ground test results conducted at Honeywell demonstrate the new principles. The Riemann-Stieltjes optimal control problem is a generalization of the unscented optimal control problem. It can be connected to many independently developed ideas across several disciplines: search theory, viability theory, quantum control and many other applications involving tychastic differential equations.

This brief details the design of a fault-tolerant control (FTC) scheme for a servohydraulic positioning system with a faulty actuator piston seal that introduces internal (crossport) leakage between the actuator chambers. It is shown that the leakage fault changes the plant type from 1 to 0, decreases the open-loop gain, and increases the effective damping. A fixed-gain linear time-invariant control law is synthesized via quantitative feedback theory (QFT) to guarantee satisfaction of a prioridefined reference tracking and stability requirements, despite the occurrence of the leakage fault. Experiments verify the ability of the designed fault-tolerant controller to compensate for the degrading effects of this fault. Experiments also demonstrate the superior tracking performance of the FTC scheme as compared to a control loop in which the effects of the leakage fault are not considered in the controller design. Index Terms-Fault-tolerant control (FTC), fluid power control, hydraulic actuators, quantitative feedback theory (QFT).

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