Marc W. McConley

A computationally efficient Lyapunov-based scheduling procedure for control of nonlinear systems with stability guarantees

We propose an alternative to gain scheduling for stabilization of nonlinear systems. For a useful class of nonlinear systems, the characterization of a region of stability based on a control Lyapunov function is computationally tractable, in the sense that computation times vary polynomially with the state dimension for a fixed number of scheduling variables. Using this fact, we develop a procedure to expand the region of stability by constructing control Lyapunov functions to various trim points of the system. A Lyapunov-based control synthesis algorithm is used to construct a control law that guarantees closed-loop stability for initial conditions in the expanded region of state space. This control asymptotically recovers the optimal stability margin in the sense of a Lyapunov derivative, which in turn can be seen as a performance measure. Robustness to bounded disturbances and stabilization under bounded control are easily incorporated into this framework. In the worst case, the computational complexity of the analysis problem that develops in the new method is increased by an exponential in the disturbance dimension. Similarly, we can handle control constraints with an increase in computational complexity of no more than an exponential in the control dimension. We demonstrate the new control design procedure on an example.

Nonlinear trajectory generation for autonomous vehicles via parameterized maneuver classes

A technique is presented for creating continuously parameterized classes of feasible system trajectories. These classes, which are useful for higher-level vehicle motion planners, follow directly from a small collection of userprovided example motions. A dynamically feasible trajectory interpolation algorithm generates a continuous family of vehicle maneuvers across a range of boundary conditions while enforcing nonlinear system equations of motion as well as nonlinear equality and inequality constraints. The scheme is particularly useful for describing motions that deviate widely from the range of linearized dynamics and where satisfactory example motions may be found from off-line nonlinear programming solutions or motion capture of human-piloted flight. The interpolation algorithm is computationally efficient, making it a viable method for real-time maneuver synthesis, particularly when used in concert with a vehicle motion planner. Experimental application to a three-degree-of-freedom rotorcraft test bed demonstrates the essential features of system and trajectory modeling, maneuver example selection, maneuver class synthesis, and integration into a hybrid system path planner.

Band-Limited Guidance and Control of Large Parafoils

* Principal member of the Technical Staff, Decision Systems Group, MS 15, Member AIAA. † Principal member of the Technical Staff, Aerospace Guidance and Control Group, MS 70, Member AIAA. ‡ Member of the Technical Staff II, Tactics, Guidance, and Control Group, MS 77. § Senior member of the Technical Staff, Cognitive Robotics Group, MS 77. ** Principal member of the Technical Staff, Manned Space Systems Group, MS 70, Member AIAA. †† Senior member of the Technical Staff, Vehicle and Robotics Group, MS 23, Member AIAA. ‡‡ Principal member of the Technical Staff, Navigation and Localization Group, MS 77. §§ Principal member of the Technical Staff, Tactical Systems Program Office, MS 79. *** Aerospace Engineer, NSRDEC, 15 Kansas Street, Senior Member AIAA. ††† Team Leader, NSRDEC, 15 Kansas Street, Member AIAA. 20th AIAA Aerodynamic Decelerator Systems Technology Conference and Seminar 4 7 May 2009, Seattle, Washington AIAA 2009-2981

A control Lyapunov function approach to robust stabilization of nonlinear systems

We propose an alternative to gain scheduling for stabilizing a class of nonlinear systems. The computation times required to find stability regions for a given control Lyapunov function vary polynomially with the state dimension for a fixed number of scheduling variables. Control Lyapunov functions to various trim points are used to expand the stability region, and a Lyapunov based synthesis formula yields a control law guaranteeing stability over this region. Robustness to bounded disturbances is easily handled, and the optimal stability margin, defined as a Lyapunov derivative, is recovered asymptotically. We apply the procedure to an example.

Hybrid control for aggressive maneuvering of autonomous aerial vehicles

New advances in control theory are required to enable aggressive maneuvering of autonomous vehicles, while adapting in real time to changes in the operational environment. A hybrid control architecture, the states of which represent feasible trajectory primitives, is constructed to reduce the complexity of the motion-planning problem for a nonlinear, high-dimensional system such as an aerial vehicle. Any feasible trajectories in the primitive list are available to the automatic control system; these may include a complete set of transitions between pairs of trim trajectories in addition to pilot-inspired behaviors recorded during manual flight tests with a human pilot. This paper describes the structure of a hybrid automaton that solves a time-optimal motion-planning problem by sequencing maneuvers in real time from such a primitive list. The algorithm can be used in a free workspace, or in the presence of fixed or moving obstacles. We present simulation results showing the effectiveness of this approach for a behavior library generated by a combination of analysis and live flight tests with a small remote-controlled helicopter.

Neural signal processing and closed-loop control algorithm design for an implanted neural recording and stimulation system.

A fully autonomous intracranial device is built to continually record neural activities in different parts of the brain, process these sampled signals, decode features that correlate to behaviors and neuropsychiatric states, and use these features to deliver brain stimulation in a closed-loop fashion. In this paper, we describe the sampling and stimulation aspects of such a device. We first describe the signal processing algorithms of two unsupervised spike sorting methods. Next, we describe the LFP time-frequency analysis and feature derivation from the two spike sorting methods. Spike sorting includes a novel approach to constructing a dictionary learning algorithm in a Compressed Sensing (CS) framework. We present a joint prediction scheme to determine the class of neural spikes in the dictionary learning framework; and, the second approach is a modified OSort algorithm which is implemented in a distributed system optimized for power efficiency. Furthermore, sorted spikes and time-frequency analysis of LFP signals can be used to generate derived features (including cross-frequency coupling, spike-field coupling). We then show how these derived features can be used in the design and development of novel decode and closed-loop control algorithms that are optimized to apply deep brain stimulation based on a patients neuropsychiatric state. For the control algorithm, we define the state vector as representative of a patients impulsivity, avoidance, inhibition, etc. Controller parameters are optimized to apply stimulation based on the state vectors current state as well as its historical values. The overall algorithm and software design for our implantable neural recording and stimulation system uses an innovative, adaptable, and reprogrammable architecture that enables advancement of the state-of-the-art in closed-loop neural control while also meeting the challenges of system power constraints and concurrent development with ongoing scientific research designed to define brain network connectivity and neural network dynamics that vary at the individual patient level and vary over time.

Polytopic control Lyapunov functions for robust stabilization of a class of nonlinear systems

Abstract We develop a method for computing a region in state space over which a nonlinear system is guaranteed by a given polytopic control Lyapunov function to be stable in closed loop under some appropriate control law. For systems which are nonlinear in only a few state variables, the procedure is computationally tractable; the computation time required to evaluate stability over each cone comprising a level set of the Lyapunov function is exponential in the number of “nonlinear states” but otherwise polynomial in the dimension of the full state space. Control constraints and robustness to bounded disturbances are easily incorporated.

A separate bias U–D factorization filter

Two forms of Friedlands separate bias estimation algorithm with U-D factorization of the covariance matrices are provided. Each is suited to implementation in a particular computing environment. (We consider MATLAB and compiled computer languages.) We reduce the computation time substantially, primarily at the time propagation stage, by using a separated bias formulation, while retaining the desirable numerical properties of the U-D factorization. The perecentage reduction typically increases with ratio of bias state dimension to dynamic state dimension. A numerical evaluation is given for the MATLAB algorithm.