Modeling kinematic variability reveals displacement and velocity based dual control of saccadic eye movements.

Noise is a ubiquitous component of motor systems that leads to behavioral variability of all types of movements. Nonetheless, systems-based models investigating human movements are generally deterministic and explain only the central tendencies like mean trajectories. In this paper, a novel approach to modeling kinematic variability of movements is presented and tested on the oculomotor system. This approach reconciles the two prominent philosophies of saccade control: displacement-based control versus velocity-based control. This was achieved by quantifying the variability in saccadic eye movements and developing a stochastic model of its control. The proposed stochastic dual model generated significantly better fits of inter-trial variances of the saccade trajectories compared to existing models. These results suggest that the saccadic system can flexibly use the information of both desired displacement and velocity for its control. This study presents a potential framework for investigating computational principles of motor control in the presence of noise utilizing stochastic modeling of kinematic variability.

Velocity tracking control best explains the modulation of saccade kinematics during eye-hand coordination.

Fast movements like saccadic eye movements that occur in the absence of sensory feedback are thought to be controlled by internal feedback. Such internal feedback provides an instantaneous estimate of the output, which serves as a proxy for sensory feedback, that can be used by the controller to correct deviations from the desired plan. In the predominant view, the desired plan/input is encoded in the form of a static displacement signal (endpoint model), believed to be encoded in the spatial map of the superior colliculus (SC). However, recent evidence has shown that SC neurons have a dynamic signal that correlates with saccade velocity, suggesting that information for velocity-based control is available for generating saccades. Motivated by this observation, we used a novel optimal control framework to test whether saccadic execution could be achieved by tracking a dynamic velocity signal at the input. We validated this velocity tracking model in a task where the peak saccade velocity was modulated by the speed of a concurrent hand movement independent of the saccade endpoint. A comparison showed that in this task, the velocity tracking model performed significantly better than the endpoint model. These results suggest that the saccadic system may have additional flexibility to incorporate a velocity-based internal feedback control when imposed by task goals or context.

A patient-specific therapeutic approach for tumour cell population extinction and drug toxicity reduction using control systems-based dose-profile design.

BACKGROUND: When anti-tumour therapy is administered to a tumour-host environment, an asymptotic tapering extremity of the tumour cell distribution is noticed. This extremity harbors a small number of residual tumour cells that later lead to secondary malignances. Thus, a method is needed that would enable the malignant population to be completely eliminated within a desired time-frame, negating the possibility of recurrence and drug-induced toxicity. METHODS: In this study, we delineate a computational procedure using the inverse input-reconstruction approach to calculate the unknown drug stimulus input, when one desires a known output tissue-response (full tumour cell elimination, no excess toxicity). The asymptotic extremity is taken care of using a bias shift of tumour-cell distribution and guided control of drug administration, with toxicity limits enforced, during mutually-synchronized chemotherapy (as Temozolomide) and immunotherapy (Interleukin-2 and Cytotoxic T-lymphocyte). RESULTS: Quantitative modeling is done using representative characteristics of rapidly and slowly-growing tumours. Both were fully eliminated within 2 months with checks for recurrence and toxicity over a two-year time-line. The dose-time profile of the therapeutic agents has similar features across tumours: biphasic (lymphocytes), monophasic (chemotherapy) and stationary (interleukin), with terminal pulses of the three agents together ensuring elimination of all malignant cells. The model is then justified with clinical case studies and animal models of different neurooncological tumours like glioma, meningioma and glioblastoma. CONCLUSION: The conflicting oncological objectives of tumour-cell extinction and host protection can be simultaneously accommodated using the techniques of drug input reconstruction by enforcing a bias shift and guided control over the drug dose-time profile. For translational applicability, the procedure can be adapted to accommodate varying patient parameters, and for corrective clinical monitoring, to implement full tumour extinction, while maintaining the health profile of the patient.

Robust/optimal temperature profile control of a high-speed aerospace vehicle using neural networks.

An approximate dynamic programming (ADP)-based suboptimal neurocontroller to obtain desired temperature for a high-speed aerospace vehicle is synthesized in this paper. A 1-D distributed parameter model of a fin is developed from basic thermal physics principles. "Snapshot" solutions of the dynamics are generated with a simple dynamic inversion-based feedback controller. Empirical basis functions are designed using the "proper orthogonal decomposition" (POD) technique and the snapshot solutions. A low-order nonlinear lumped parameter system to characterize the infinite dimensional system is obtained by carrying out a Galerkin projection. An ADP-based neurocontroller with a dual heuristic programming (DHP) formulation is obtained with a single-network-adaptive-critic (SNAC) controller for this approximate nonlinear model. Actual control in the original domain is calculated with the same POD basis functions through a reverse mapping. Further contribution of this paper includes development of an online robust neurocontroller to account for unmodeled dynamics and parametric uncertainties inherent in such a complex dynamic system. A neural network (NN) weight update rule that guarantees boundedness of the weights and relaxes the need for persistence of excitation (PE) condition is presented. Simulation studies show that in a fairly extensive but compact domain, any desired temperature profile can be achieved starting from any initial temperature profile. Therefore, the ADP and NN-based controllers appear to have the potential to become controller synthesis tools for nonlinear distributed parameter systems.

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 single network adaptive critic (SNAC) architecture for optimal control synthesis for a class of nonlinear systems.

Even though dynamic programming offers an optimal control solution in a state feedback form, the method is overwhelmed by computational and storage requirements. Approximate dynamic programming implemented with an Adaptive Critic (AC) neural network structure has evolved as a powerful alternative technique that obviates the need for excessive computations and storage requirements in solving optimal control problems. In this paper, an improvement to the AC architecture, called the "Single Network Adaptive Critic (SNAC)" is presented. This approach is applicable to a wide class of nonlinear systems where the optimal control (stationary) equation can be explicitly expressed in terms of the state and costate variables. The selection of this terminology is guided by the fact that it eliminates the use of one neural network (namely the action network) that is part of a typical dual network AC setup. As a consequence, the SNAC architecture offers three potential advantages: a simpler architecture, lesser computational load and elimination of the approximation error associated with the eliminated network. In order to demonstrate these benefits and the control synthesis technique using SNAC, two problems have been solved with the AC and SNAC approaches and their computational performances are compared. One of these problems is a real-life Micro-Electro-Mechanical-system (MEMS) problem, which demonstrates that the SNAC technique is applicable to complex engineering systems.

Feedback linearization based computer controlled medication design for automatic treatment of parturient paresis of cows.

Based on an existing model for calcium homeostatis (dynamics) and taking the help of feedback linearization philosophy of nonlinear control theory, two control design (medication) strategies are presented for automatic treatment of parturient paresis (milk fever) disease of cows. An important advantage of the new approach is that it results in a simple and straightforward method and eliminates the necessity of a significantly more complex neural network based nonlinear optimal control technique, as proposed by the author earlier. As an added advantage, unlike the neural network technique, the new approach leads to 'closed form solution' for the nonlinear controller. Moreover, global asymptotic stability of the closed loop system is always guaranteed. Besides theoretical justifications, the resulting controllers (medication strategies) are validated from numerical simulation studies of the nonlinear system as well. Moreover, from a numerical study about the robustness of the algorithms with respect to parametric uncertainty, it was observed that the optimal control formulation is a better option over the dynamic inversion formulation.

Proper orthogonal decomposition based optimal neurocontrol synthesis of a chemical reactor process using approximate dynamic programming.

The concept of approximate dynamic programming and adaptive critic neural network based optimal controller is extended in this study to include systems governed by partial differential equations. An optimal controller is synthesized for a dispersion type tubular chemical reactor, which is governed by two coupled nonlinear partial differential equations. It consists of three steps: First, empirical basis functions are designed using the 'Proper Orthogonal Decomposition' technique and a low-order lumped parameter system to represent the infinite-dimensional system is obtained by carrying out a Galerkin projection. Second, approximate dynamic programming technique is applied in a discrete time framework, followed by the use of a dual neural network structure called adaptive critics, to obtain optimal neurocontrollers for this system. In this structure, one set of neural networks captures the relationship between the state variables and the control, whereas the other set captures the relationship between the state and the costate variables. Third, the lumped parameter control is then mapped back to the spatial dimension using the same basis functions to result in a feedback control. Numerical results are presented that illustrate the potential of this approach. It should be noted that the procedure presented in this study can be used in synthesizing optimal controllers for a fairly general class of nonlinear distributed parameter systems.

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.