Effective treatment of infectious diseases: A nonlinear adaptive control theoretic approach

A nonlinear adaptive system theoretic approach is presented in this paper for effective treatment of infectious diseases that affect various organs of the human body. The generic model used does not represent any specific disease. However, it mimics the generic immunological dynamics of the human body under pathological attack, including the response to external drugs. From a system theoretic point of view, drugs can be interpreted as control inputs. Assuming a set of nominal parameters in the mathematical model, first a nonlinear controller is designed based on the principle of dynamic inversion. This treatment strategy was found to be effective in completely curing "nominal patients". However, in some cases it is ineffective in curing "realistic patients". This leads to serious (sometimes fatal) damage to the affected organ. To make the drug dosage design more effective, a model-following neuro-adaptive control design is carried out using neural networks, which are trained (adapted) online. From simulation studies, this adaptive controller is found to be effective in killing the invading microbes and healing the damaged organ even in the presence of parameter uncertainties and continuing pathogen attack.

On the Milito-Cruz adaptive control scheme for Markov chains

Milito and Cruz have introduced a novel adaptive control scheme for finite Markov chains when a finite parametrized family of possible transition matrices is available. The scheme involves the minimization of a composite functional of the observed history of the process incorporating both control and estimation aspects. We prove the a.s. optimality of a similar scheme when the state space is countable and the parameter space a compact subset ofR.

Adaptive control of vibration transmission in a strut system

In this article, theoretical and the experimental studies are reported on the adaptive control of vibration transmission in a strut system subjected to a longitudinal pulse train excitation. In the control scheme, a magneto-strictive actuator is employed at the downstream transmission point in the secondary path. The actuator dynamics is taken into account. The system boundary parameters are first estimated off-line, and later employed to simulate the system dynamics. A Delayed-X Filtered-E spectral algorithm is proposed and implemented in real time. The underlying mechanics based filter construction allows for the time varying system dynamics to be taken into account. This work should be of interest for active control of vibration and noise transmission in helicopter gearbox support struts and other systems.

Reinforcement learning with average cost for adaptive control of traffic lights at intersections

We propose for the first time two reinforcement learning algorithms with function approximation for average cost adaptive control of traffic lights. One of these algorithms is a version of Q-learning with function approximation while the other is a policy gradient actor-critic algorithm that incorporates multi-timescale stochastic approximation. We show performance comparisons on various network settings of these algorithms with a range of fixed timing algorithms, as well as a Q-learning algorithm with full state representation that we also implement. We observe that whereas (as expected) on a two-junction corridor, the full state representation algorithm shows the best results, this algorithm is not implementable on larger road networks. The algorithm PG-AC-TLC that we propose is seen to show the best overall performance.

Convergence problems in a class of model reference adaptive control systems

A class of model reference adaptive control system which make use of an augmented error signal has been introduced by Monopoli. Convergence problems in this attractive class of systems have been investigated in this paper using concepts from hyperstability theory. It is shown that the condition on the linear part of the system has to be stronger than the one given earlier. A boundedness condition on the input to the linear part of the system has been taken into account in the analysis - this condition appears to have been missed in the previous applications of hyperstability theory. Sufficient conditions for the convergence of the adaptive gain to the desired value are also given.

Adaptive load control of the central processor in a distributed system with a star topology

The author presents adaptive control techniques for controlling the flow of real-time jobs from the peripheral processors (PPs) to the central processor (CP) of a distributed system with a star topology. He considers two classes of flow control mechanisms: (1) proportional control, where a certain proportion of the load offered to each PP is sent to the CP, and (2) threshold control, where there is a maximum rate at which each PP can send jobs to the CP. The problem is to obtain good algorithms for dynamically adjusting the control level at each PP in order to prevent overload of the CP, when the load offered by the PPs is unknown and varying. The author formulates the problem approximately as a standard system control problem in which the system has unknown parameters that are subject to change. Using well-known techniques (e.g., naive-feedback-controller and stochastic approximation techniques), he derives adaptive controls for the system control problem. He demonstrates the efficacy of these controls in the original problem by using the control algorithms in simulations of a queuing model of the CP and the load controls.

A Neuro-Adaptive Approach for Robust Control of High Performance Aircrafts with Parameter Inaccuracies

For high performance aircrafts, the flight control system needs to be quite effective in both assuring accurate tracking of pilot commands, while simultaneously assuring overall stability of the aircraft. In addition, the control system must also be sufficiently robust to cater to possible parameter variations. The primary aim of this paper is to enhance the robustness of the controller for a HPA using neuro-adaptive control design. Here the architecture employs a network of Gaussian Radial basis functions to adaptively compensate for the ignored system dynamics. A stable weight mechanism is determined using Lyapunov theory. The network construction and performance of the resulting controller are illustrated through simulations with a low-fidelity six –DOF model of F16 that is available in open literature.

Model-following Neuro-adaptive approach for robust control of high performance aircrafts

Based on dynamic inversion, a relatively straightforward approach is presented in this paper for nonlinear flight control design of high performance aircrafts, which does not require the normal and lateral acceleration commands to be first transferred to body rates before computing the required control inputs. This leads to substantial improvement of the tracking response. Promising results are obtained from six degree-offreedom simulation studies of F-16 aircraft, which are found to be superior as compared to an existing approach (which is also based on dynamic inversion). The new approach has two potential benefits, namely reduced oscillatory response (including elimination of non-minimum phase behavior) and reduced control magnitude. Next, a model-following neuron-adaptive design is augmented the nominal design in order to assure robust performance in the presence of parameter inaccuracies in the model. Note that in the approach the model update takes place adaptively online and hence it is philosophically similar to indirect adaptive control. However, unlike a typical indirect adaptive control approach, there is no need to update the individual parameters explicitly. Instead the inaccuracy in the system output dynamics is captured directly and then used in modifying the control. This leads to faster adaptation, which helps in stabilizing the unstable plant quicker. The robustness study from a large number of simulations shows that the adaptive design has good amount of robustness with respect to the expected parameter inaccuracies in the model.

Adaptive Flight-Control Design Using Neural-Network-Aided Optimal Nonlinear Dynamic Inversion

A neural-network-aided nonlinear dynamic inversion-based hybrid technique of model reference adaptive control flight-control system design is presented in this paper. Here, the gains of the nonlinear dynamic inversion-based flight-control system are dynamically selected in such a manner that the resulting controller mimics a single network, adaptive control, optimal nonlinear controller for state regulation. Traditional model reference adaptive control methods use a linearized reference model, and the presented control design method employs a nonlinear reference model to compute the nonlinear dynamic inversion gains. This innovation of designing the gain elements after synthesizing the single network adaptive controller maintains the advantages that an optimal controller offers, yet it retains a simple closed-form control expression in state feedback form, which can easily be modified for tracking problems without demanding any a priori knowledge of the reference signals. The strength of the technique is demonstrated by considering the longitudinal motion of a nonlinear aircraft system. An extended single network adaptive control/nonlinear dynamic inversion adaptive control design architecture is also presented, which adapts online to three failure conditions, namely, a thrust failure, an elevator failure, and an inaccuracy in the estimation of C-M alpha. Simulation results demonstrate that the presented adaptive flight controller generates a near-optimal response when compared to a traditional nonlinear dynamic inversion controller.

An adaptive drug delivery design using neural networks for effective treatment of infectious diseases: A simulation study

An adaptive drug delivery design is presented in this paper using neural networks for effective treatment of infectious diseases. The generic mathematical model used describes the coupled evolution of concentration of pathogens, plasma cells, antibodies and a numerical value that indicates the relative characteristic of a damaged organ due to the disease under the influence of external drugs. From a system theoretic point of view, the external drugs can be interpreted as control inputs, which can be designed based on control theoretic concepts. In this study, assuming a set of nominal parameters in the mathematical model, first a nonlinear controller (drug administration) is designed based on the principle of dynamic inversion. This nominal drug administration plan was found to be effective in curing "nominal model patients" (patients whose immunological dynamics conform to the mathematical model used for the control design exactly. However, it was found to be ineffective in curing "realistic model patients" (patients whose immunological dynamics may have off-nominal parameter values and possibly unwanted inputs) in general. Hence, to make the drug delivery dosage design more effective for realistic model patients, a model-following adaptive control design is carried out next by taking the help of neural networks, that are trained online. Simulation studies indicate that the adaptive controller proposed in this paper holds promise in killing the invading pathogens and healing the damaged organ even in the presence of parameter uncertainties and continued pathogen attack. Note that the computational requirements for computing the control are very minimal and all associated computations (including the training of neural networks) can be carried out online. However it assumes that the required diagnosis process can be carried out at a sufficient faster rate so that all the states are available for control computation.

An optimal dynamic inversion-based neuro-adaptive approach for treatment of chronic myelogenous leukemia

Combining the advanced techniques of optimal dynamic inversion and model-following neuro-adaptive control design, an innovative technique is presented to design an automatic drug administration strategy for effective treatment of chronic myelogenous leukemia (CML). A recently developed nonlinear mathematical model for cell dynamics is used to design the controller (medication dosage). First, a nominal controller is designed based on the principle of optimal dynamic inversion. This controller can treat the nominal model patients (patients who can be described by the mathematical model used here with the nominal parameter values) effectively. However, since the system parameters for a realistic model patient can be different from that of the nominal model patients, simulation studies for such patients indicate that the nominal controller is either inefficient or, worse, ineffective; i.e. the trajectory of the number of cancer cells either shows non-satisfactory transient behavior or it grows in an unstable manner. Hence, to make the drug dosage history more realistic and patient-specific, a model-following neuro-adaptive controller is augmented to the nominal controller. In this adaptive approach, a neural network trained online facilitates a new adaptive controller. The training process of the neural network is based on Lyapunov stability theory, which guarantees both stability of the cancer cell dynamics as well as boundedness of the network weights. From simulation studies, this adaptive control design approach is found to be very effective to treat the CML disease for realistic patients. Sufficient generality is retained in the mathematical developments so that the technique can be applied to other similar nonlinear control design problems as well.

A neuro-adaptive augmented optimal dynamic inversion approach for effective and efficient treatment of chronic myelogenous leukemia

Combining the advanced techniques of optimal dynamic inversion and model-following neuro-adaptive control design, an efficient technique is presented for effective treatment of chronic myelogenous leukemia (CML). A recently developed nonlinear mathematical model for cell dynamics is used for the control (medication) synthesis. First, taking a set of nominal parameters, a nominal controller is designed based on the principle of optimal dynamic inversion. This controller can treat nominal patients (patients having same nominal parameters as used for the control design) effectively. However, since the parameters of an actual patient can be different from that of the ideal patient, to make the treatment strategy more effective and efficient, a model-following neuro-adaptive controller is augmented to the nominal controller. In this approach, a neural network trained online (based on Lyapunov stability theory) facilitates a new adaptive controller, computed online. From the simulation studies, this adaptive control design approach (treatment strategy) is found to be very effective to treat the CML disease for actual patients. Sufficient generality is retained in the theoretical developments in this paper, so that the techniques presented can be applied to other similar problem as well. Note that the technique presented is computationally non-intensive and all computations can be carried out online.

Adaptive optimal tuning of a general class of stable LTI systems with restricted inputs

The problem addressed is one of model reference adaptive control (MRAC) of asymptotically stable plants of unknown order with zeros located anywhere in the s-plane except at the origin. The reference model is also asymptotically stable and lacking zero(s) at s = 0. The control law is to be specified only in terms of the inputs to and outputs of the plant and the reference model. For inputs from a class of functions that approach a non-zero constant, the problem is formulated in an optimal control framework. By successive refinements of the sub-optimal laws proposed here, two schemes are finally design-ed. These schemes are characterized by boundedness, convergence and optimality. Simplicity and total time-domain implementation are the additional striking features. Simulations to demonstrate the efficacy of the control schemes are presented.

An adaptive cascade compensator for a wide class of stable minimum or nonminimum phase plants through time moment estimation

Model Reference Adaptive Control (MRAC) of a wide repertoire of stable Linear Time Invariant (LTI) systems is addressed here. Even an upper bound on the order of the finite-dimensional system is unavailable. Further, the unknown plant is permitted to have both minimum phase and nonminimum phase zeros. Model following with reference to a completely specified reference model excited by a class of piecewise continuous bounded signals is the goal. The problem is approached by taking recourse to the time moments representation of an LTI system. The treatment here is confined to Single-Input Single-Output (SISO) systems. The adaptive controller is built upon an on-line scheme for time moment estimation of a system given no more than its input and output. As a first step, a cascade compensator is devised. The primary contribution lies in developing a unified framework to eventually address with more finesse the problem of adaptive control of a large family of plants allowed to be minimum or nonminimum phase. Thus, the scheme presented in this paper is confined to lay the basis for more refined compensators-cascade, feedback and both-initially for SISO systems and progressively for Multi-Input Multi-Output (MIMO) systems. Simulations are presented.

A smart approach to precision attitude maneuvers of spacecrafts

A nonlinear adaptive approach is presented to achieve rest-to-rest attitude maneuvers for spacecrafts in the presence of parameter uncertainties and unknown disturbances. A nonlinear controller, designed on the principle of dynamic inversion achieves the goals for the nominal model but suffers performance degradation in the presence of off-nominal parameter values and unwanted inputs. To address this issue, a model-following neuro-adaptive control design is carried out by taking the help of neural networks. Due to the structured approach followed here, the adaptation is restricted to the momentum level equations.The adaptive technique presented is computationally nonintensive and hence can be implemented in real-time. Because of these features, this new approach is named as structured model-following adaptive real-time technique (SMART). From simulation studies, this SMART approach is found to be very effective in achieving precision attitude maneuvers in the presence of parameter uncertainties and unknown disturbances.