Optimal control of nonlinear continuous-time systems in strict-feedback form.

This paper proposes a novel optimal tracking control scheme for nonlinear continuous-time systems in strict-feedback form with uncertain dynamics. The optimal tracking problem is transformed into an equivalent optimal regulation problem through a feedforward adaptive control input that is generated by modifying the standard backstepping technique. Subsequently, a neural network-based optimal control scheme is introduced to estimate the cost, or value function, over an infinite horizon for the resulting nonlinear continuous-time systems in affine form when the internal dynamics are unknown. The estimated cost function is then used to obtain the optimal feedback control input; therefore, the overall optimal control input for the nonlinear continuous-time system in strict-feedback form includes the feedforward plus the optimal feedback terms. It is shown that the estimated cost function minimizes the Hamilton-Jacobi-Bellman estimation error in a forward-in-time manner without using any value or policy iterations. Finally, optimal output feedback control is introduced through the design of a suitable observer. Lyapunov theory is utilized to show the overall stability of the proposed schemes without requiring an initial admissible controller. Simulation examples are provided to validate the theoretical results.

Zero-sum two-player game theoretic formulation of affine nonlinear discrete-time systems using neural networks.

In this paper, the nearly optimal solution for discrete-time (DT) affine nonlinear control systems in the presence of partially unknown internal system dynamics and disturbances is considered. The approach is based on successive approximate solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which appears in optimal control. Successive approximation approach for updating control and disturbance inputs for DT nonlinear affine systems are proposed. Moreover, sufficient conditions for the convergence of the approximate HJI solution to the saddle point are derived, and an iterative approach to approximate the HJI equation using a neural network (NN) is presented. Then, the requirement of full knowledge of the internal dynamics of the nonlinear DT system is relaxed by using a second NN online approximator. The result is a closed-loop optimal NN controller via offline learning. A numerical example is provided illustrating the effectiveness of the approach.

Online optimal control of affine nonlinear discrete-time systems with unknown internal dynamics by using time-based policy update.

In this paper, the Hamilton-Jacobi-Bellman equation is solved forward-in-time for the optimal control of a class of general affine nonlinear discrete-time systems without using value and policy iterations. The proposed approach, referred to as adaptive dynamic programming, uses two neural networks (NNs), to solve the infinite horizon optimal regulation control of affine nonlinear discrete-time systems in the presence of unknown internal dynamics and a known control coefficient matrix. One NN approximates the cost function and is referred to as the critic NN, while the second NN generates the control input and is referred to as the action NN. The cost function and policy are updated once at the sampling instant and thus the proposed approach can be referred to as time-based ADP. Novel update laws for tuning the unknown weights of the NNs online are derived. Lyapunov techniques are used to show that all signals are uniformly ultimately bounded and that the approximated control signal approaches the optimal control input with small bounded error over time. In the absence of disturbances, an optimal control is demonstrated. Simulation results are included to show the effectiveness of the approach. The end result is the systematic design of an optimal controller with guaranteed convergence that is suitable for hardware implementation.

Comparison of Airtraq optical laryngoscope and Storz video laryngoscope in a cadaver model.

BACKGROUND: Airway management in the emergency department is a critical intervention that requires both standard techniques and rescue techniques to ensure a high rate of success. Recently, video laryngoscope (VL) systems have become increasingly common in many large urban EDs, but these systems may exceed the budgets of smaller rural EDs and EMS services and the Airtraq optical laryngoscope (OL) may provide an effective, low-cost alternative. We hypothesized that laryngeal view and time to endothracheal tube placement for OL and VL intubations would not be significantly different. METHODS: This was a prospective, crossover trial. SETTING: University-based emergency medicine residency program procedure laboratory utilizing lightly embalmed cadavers. SUBJECTS: PGY1-3 emergency medicine residents. The study subjects performed timed endotracheal intubations alternately using the OL and VL. The subjects then rated the Cormack-Lehane laryngeal view for each device. STATISTICAL ANALYSIS: Mean time to intubation and the mean laryngeal view score were calculated with 95% confidence intervals and statistical significance was determined by Student's t test. RESULTS: Fourteen subjects completed the study. The average laryngeal view achieved with the OL vs. the VL was not significantly different, with Cormack-Lehane grade of 1.14 vs. 1.07, respectively. Time to endotracheal intubation, however, was significantly different (P<0.001) with the average time to intubation for the OL 25.49 seconds (95% CI: 17.95-33.03) and the VL 13.41 seconds (10.27-16.55). CONCLUSION: The Airtraq OL and the Storz VL yielded similar laryngeal views in the lightly embalmed cadaver model. Time to endotracheal tube placement, however, was less for the VL.

Output feedback control of a quadrotor UAV using neural networks.

In this paper, a new nonlinear controller for a quadrotor unmanned aerial vehicle (UAV) is proposed using neural networks (NNs) and output feedback. The assumption on the availability of UAV dynamics is not always practical, especially in an outdoor environment. Therefore, in this work, an NN is introduced to learn the complete dynamics of the UAV online, including uncertain nonlinear terms like aerodynamic friction and blade flapping. Although a quadrotor UAV is underactuated, a novel NN virtual control input scheme is proposed which allows all six degrees of freedom (DOF) of the UAV to be controlled using only four control inputs. Furthermore, an NN observer is introduced to estimate the translational and angular velocities of the UAV, and an output feedback control law is developed in which only the position and the attitude of the UAV are considered measurable. It is shown using Lyapunov theory that the position, orientation, and velocity tracking errors, the virtual control and observer estimation errors, and the NN weight estimation errors for each NN are all semiglobally uniformly ultimately bounded (SGUUB) in the presence of bounded disturbances and NN functional reconstruction errors while simultaneously relaxing the separation principle. The effectiveness of proposed output feedback control scheme is then demonstrated in the presence of unknown nonlinear dynamics and disturbances, and simulation results are included to demonstrate the theoretical conjecture.

Neural network output feedback control of robot formations.

In this paper, a combined kinematic/torque output feedback control law is developed for leader-follower-based formation control using backstepping to accommodate the dynamics of the robots and the formation in contrast with kinematic-based formation controllers. A neural network (NN) is introduced to approximate the dynamics of the follower and its leader using online weight tuning. Furthermore, a novel NN observer is designed to estimate the linear and angular velocities of both the follower robot and its leader. It is shown, by using the Lyapunov theory, that the errors for the entire formation are uniformly ultimately bounded while relaxing the separation principle. In addition, the stability of the formation in the presence of obstacles, is examined using Lyapunov methods, and by treating other robots in the formation as obstacles, collisions within the formation are prevented. Numerical results are provided to verify the theoretical conjectures.

Optimal control of unknown affine nonlinear discrete-time systems using offline-trained neural networks with proof of convergence.

The optimal control of linear systems accompanied by quadratic cost functions can be achieved by solving the well-known Riccati equation. However, the optimal control of nonlinear discrete-time systems is a much more challenging task that often requires solving the nonlinear Hamilton-Jacobi-Bellman (HJB) equation. In the recent literature, discrete-time approximate dynamic programming (ADP) techniques have been widely used to determine the optimal or near optimal control policies for affine nonlinear discrete-time systems. However, an inherent assumption of ADP requires the value of the controlled system one step ahead and at least partial knowledge of the system dynamics to be known. In this work, the need of the partial knowledge of the nonlinear system dynamics is relaxed in the development of a novel approach to ADP using a two part process: online system identification and offline optimal control training. First, in the system identification process, a neural network (NN) is tuned online using novel tuning laws to learn the complete plant dynamics so that a local asymptotic stability of the identification error can be shown. Then, using only the learned NN system model, offline ADP is attempted resulting in a novel optimal control law. The proposed scheme does not require explicit knowledge of the system dynamics as only the learned NN model is needed. The proof of convergence is demonstrated. Simulation results verify theoretical conjecture.

Neural network control of mobile robot formations using RISE feedback.

In this paper, an asymptotically stable (AS) combined kinematic/torque control law is developed for leader-follower-based formation control using backstepping in order to accommodate the complete dynamics of the robots and the formation, and a neural network (NN) is introduced along with robust integral of the sign of the error feedback to approximate the dynamics of the follower as well as its leader using online weight tuning. It is shown using Lyapunov theory that the errors for the entire formation are AS and that the NN weights are bounded as opposed to uniformly ultimately bounded stability which is typical with most NN controllers. Additionally, the stability of the formation in the presence of obstacles is examined using Lyapunov methods, and by treating other robots in the formation as obstacles, collisions within the formation do not occur. The asymptotic stability of the follower robots as well as the entire formation during an obstacle avoidance maneuver is demonstrated using Lyapunov methods, and numerical results are provided to verify the theoretical conjectures.