The principles of calculus of variations are used to obtain necessary conditions for optimal control of dynamical systems that involve nonconstant time lags. Consideration is given to systems that can be represented mathematically by a finite set of ordinary nonlinear differential-difference equations with one or more time-dependent argument lags. Application of the general results to classes of linear systems with finite-time quadratic performance criteria is considered in detail. Optimal feedback control laws are given. Discussion of a proposed method for obtaining computational solutions for nonlinear systems with variable delays is included in the paper.

Optical platforms increasingly require attitude knowledge and optical instrument pointing at sub-microradian accuracy. No low-cost commercial system exists to provide this level of accuracy for guidance, navigation, and control (GN&C). The need for small, inexpensive inertial sensors, which may be employed in pointing control systems that are required to satisfy angular line-of-sight (LOS) stabilization jitter error budgets to levels of 1-3 microradian rms and less, has existed for at least two decades. Innovations and evolutions in small, low-noise inertial angular motion sensor technology and advances in the applications of the global positioning system (GPS) have converged to allow improvement in acquisition, tracking and pointing (ATP) solutions for a wide variety of payloads. We are developing a small, inexpensive, and high-performance inertial attitude reference system that uses our innovative magnetohydrodynamic (MHD) angular rate sensor (ARS) technology.The system's components are modular to allow ease in customizing the unit for specific applications. The basic system functions as a jitter-free fast steering mirror or reference laser assembly. For applications requiring an inertial pointing reference, the system can blend its ARS sensor information with GPS, gyroscope, and accelerometer data. This combination with the reference laser will produce a "virtual star" that is isolated from the vibrations and disturbances of the host platform and optical system and becomes an attitude, alignment, and stabilization reference for the payload. This paper describes the system's design, specifications, and projected performance for a variety of configurations and applications.

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The development of a computer program for the optimization of dynamic systems subject to parameter and terminal state constraints is presented in this paper. The problem is handled by converting it to an equivalent algebraic optimization problem. The resulting problem is then solved by a modified version (D YS UMT) of the nonlinear programming method S UMT (Sequential Unconstrained Minimization Technique). The available program provides an efficient and convenient analysis tool to aid engineers in the modeling and designing of dynamic systems.