Showing papers by "Robert F. Stengel published in 2002"

Optimal control of innate immune response

Abstract: Treatment of a pathogenic disease process is interpreted as the optimal control of a dynamic system. Evolution of the disease is characterized by a non-linear, fourth-order ordinary differential equation that describes concentrations of pathogens, plasma cells, and antibodies, as well as a numerical indication of patient health. Without control, the dynamic model evidences sub-clinical or clinical decay, chronic stabilization, or unrestrained lethal growth of the pathogen, depending on the initial conditions for the infection. The dynamic equations are controlled by therapeutic agents that affect the rate of change of system variables. Control histories that minimize a quadratic cost function are generated by numerical optimization over a fixed time interval, given otherwise lethal initial conditions. Tradeoffs between cost function weighting of pathogens, organ health, and use of therapeutics are evaluated. Optimal control solutions that defeat the pathogen and preserve organ health are demonstrated for four different approaches to therapy. It is shown that control theory can point the way toward new protocols for treatment and remediation of human diseases. Copyright © 2002 John Wiley & Sons, Ltd.

An adaptive critic global controller

Abstract: A nonlinear control system comprising a network of networks is taught using a two-phase learning procedure realized through novel techniques for initialization, on-line training, and adaptive critic design. The neural networks are initialized algebraically by observing that the gradients of the networks must equal corresponding linear gain matrices at chosen operating points. On-line learning is based on a dual heuristic adaptive critic architecture that improves control for large, coupled motions by accounting for plant dynamics and nonlinear effects. The result is an adaptive controller that is as conservative as the linear designs and as effective as the global controller. The design method is implemented to control the full six-degree-of-freedom simulation of a business jet aircraft.

Optimal enhancement of immune response

Abstract: MOTIVATION: Therapeutic enhancement of innate immune response to microbial attack is addressed as the optimal control of a dynamic system. Interactions between an invading pathogen and the innate immune system are characterized by four non-linear, ordinary differential equations that describe rates of change of pathogen, plasma cell, and antibody concentrations, and of an indicator of organic health. Without therapy, the dynamic model evidences sub-clinical or clinical decay, chronic stabilization, or unrestrained lethal growth of the pathogen; the response pattern depends on the initial concentration of pathogens in the simulated attack. In the model, immune response can be augmented by therapeutic agents that kill the pathogen directly, that stimulate the production of plasma cells or antibodies, or that enhance organ health. A previous paper demonstrated open-loop optimal control solutions that defeat the pathogen and preserve organ health, given initial conditions that otherwise would be lethal (Stengel et al. (2002)). Therapies based on separate and combined application of the agents were derived by minimizing a quadratic cost function that weighted both system response and control usage, providing implicit control over harmful side effects. RESULTS: We demonstrate the ability of neighboring-optimal feedback control to account for a range of unknown initial conditions and persistent input of pathogens by adjusting the therapy to account for perturbations from the nominal-optimal response history. We examine therapies that combine open-loop control of one agent with closed-loop control of another. We show that optimal control theory points the way toward new protocols for treatment and cure of human diseases. CONTACT: stengel@princeton.edu; rghiglia@princeton.edu; nkulkarn@princeton.edu

Classical/Neural Synthesis of Nonlinear Control Systems

Abstract: Classical/neural synthesis of control systems combines the most effective elements of old and new design concepts with the promise of producing better control systems. There is considerable precedent for applying gain-scheduled linear controllers to nonlinear systems, especially those that can be locally approximated as linear-parameter-varying systems; however, a means for transferring the insights gained from these linear controllers to nonlinear controllers remains to be identified. The approach taken here is to design nonlinear control systems that take advantage of prior knowledge and experience gained from linear controllers, while capitalizing on the broader capabilities of adaptive, nonlinear control theory and computational neural networks. Central to this novel approach is the recognition that the gradients of a nonlinear control law must represent the gain matrices of an equivalent, locally linearized controller. In this paper we focus on the initial specification for the control law, which consists of a set of hypersurfaces expressed as neural networks that represent satisfactory linear controllers designed over the plant's operating range. Along the way, a new neural network training method consisting solely of solving algebraic linear systems of equations is developed, and its effectiveness is demonstrated on a case study.