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This paper presents a new out-of-step detection method for multi-machine power systems based on approximate stability boundaries. The boundaries are constructed based on Zubov's method of stability analysis. The proposed out-of-step detection method first constructs a series of boundaries in power angle - frequency (δ-ω) plane, and tracks the trajectory of each generator in the δ-ω plane after the...
This paper demonstrates, how an approximation of the costate trajectory can be obtained for switched systems with state jumps, when an optimal control problem with fixed switching sequence is solved using a direct method, i.e. direct shooting or collocation. The obtained trajectories include the jump conditions for the costate given by necessary conditions for optimal control of switched systems.
The paper deals with the sampled-data implementation of controllers designed by means of Immersion and Invariance stabilization techniques for a special class of dynamics. A multi-rate digital control law is derived to preserve at the sampling instants manifold attractivity. The immersion condition is guaranteed under sampling and invariance on the manifold is recovered asymptotically by the multi-rate...
The paper shows analogies between two separately evolved areas of PID control, the disturbance observer based controllers and the “intelligent” PID controllers. The simplest “intelligent” PID controller is represented by the “intelligent P” controller denoted as iP. It is designed for the simplified “ultra-local” integral plant models neglecting all internal plant feedbacks. These are included and...
In this paper we propose to track online computed force trajectories to control the energy of various types of pendulum-like objects. The considered pendulum-like objects can be controlled by multiple agents and swing in different oscillation degrees of freedom. Our goal is to excite one specific oscillation, the intended oscillation, while damping all other disturbance oscillations. By approximating...
A prerequisite to safe robot motion is to avoid Inevitable Collision States (ICS). However, the characterization of the ICS set is a challenge. Several approximation methods have been proposed, most of which either are overly conservative or fail to provide proper motion safety guarantees. In order to to improve safety guarantees, we build upon Viability Theory and adapt an algorithm designed to approximate...
In this paper we investigate the monotonicity of various optimality criteria during the exploration phase of an active SLAM algorithm. Optimality criteria such as A-opt, D-opt or E-opt are used in active SLAM to account for uncertainty in the map or the robot's pose, and these criteria are usually part of utility functions which help active SLAM algorithms decide where the robot should move next....
This paper considers the problem of approximating a kernel matrix in an autoregressive Gaussian process regression (AR-GP) in the presence of measurement noises or natural errors for modeling complex motions of pedestrians in a crowded environment. While a number of methods have been proposed to robustly predict future motions of humans, it still remains as a difficult problem in the presence of measurement...
This paper presents a multiagent path planning algorithm based on sequential convex programming (SCP) that finds locally optimal trajectories. Previous work using SCP efficiently computes motion plans in convex spaces with no static obstacles. In many scenarios where the spaces are non-convex, previous SCP-based algorithms failed to find feasible solutions because the convex approximation of collision...
This paper introduces an approximate analytical solution to the otherwise non-integrable double-stance dynamics of the bipedal spring-loaded inverted pendulum (SLIP). Despite the apparent structural simplicity of the SLIP, the exact analytical solution to its stance dynamics cannot be found. Approximate maps have been proposed for the monoped SLIP runner (encompassing a single-stance phase). Still,...
This paper addresses the tracking problem using the short state sequences in time series (which is called plot-sequences in this paper) obtained from multi-frame track-before-detect (TBD). Some TBD methods, e.g., dynamic programming (DP), maximum likelihood probabilistic data association (ML-PDA), histogram probabilistic multihypothesis tracker (H-PMHT) and Hough transform (HT) based TBD, are batch...
This paper presents adaptive neural tracking control for a class of uncertain single-input single-output (SISO) non-affine nonlinear systems in general form. To deal with the non-affine appearance of the control variables, the Taylor series expansion is employed to transform the systems into a block-triangular affine form in the neighborhood of the ideal unknown control law. The developed neural control...
This paper proposes an algorithmic modeling and analysis method to study the dynamics of nonlinear biological systems. Motivated by the recent use of piecewise affine models in reachability analysis of continuous dynamical systems, we propose a multi-affine approximation method to study biological system models defined on hyperrectangle. We show that such approximation is useful for constructing system's...
This paper focusses on the strange nature and qualitative behavior associated with the systems characterized by State Dependent-Delay Differential Equations (SD-DDEs). We consider one of the most simple and innocently looking SD-DDEs x(t) = ±x(t-x(t)). This retarded SD-DDE brings a lot of intricacies. It looks linear but is actually a nonlinear SD-DDE in disguise. It exhibits the phenomenon of bifurcation...
We present an algorithm for resampling data from a non-uniform grid onto a uniform grid. Our algorithm termed generalized sparse uniform resampling (GSURS) uses methods from modern sampling theory. Selection of an intermediate subspace generated by integer translations of a compactly supported generating kernel produces a sparse system of equations representing the relation between the nonuniformly...
Parametric filters, such as the Extended Kalman Filter and the Unscented Kalman Filter, typically scale well with the dimensionality of the problem, but they are known to fail if the posterior state distribution cannot be closely approximated by a density of the assumed parametric form.
This paper deals with the generation of motion for complex dynamical systems (such as humanoid robots) to achieve several concurrent objectives. Hierarchy of tasks and optimal control are two frameworks commonly used to this aim. The first one specifies control objectives as a number of quadratic functions to be minimized under strict priorities. The second one minimizes an arbitrary user-defined...
This paper reformulates an optimization algorithm previously presented in continuous-time to one using structured integration and structured linearization methods from discrete mechanics. The objective is to synthesize trajectories for dynamic robotic systems that improve the estimation of model parameters by using a metric on Fisher information in a nonlinear projection-based trajectory optimization...
What is it that makes movement around obstacles hard? The answer seems clear: obstacles contort the geometry of the workspace and make it difficult to leverage what we consider easy and intuitive straight-line Cartesian geometry. But is Cartesian motion actually easy? It's certainly well-understood and has numerous applications. But beneath the details of linear algebra and pseudoinverses, lies a...
Ensuring safety in partially-known environments is a critical problem in robotics since the environment is perceived through sensors and the environment cannot be completely known ahead of time. Prior work has considered the problem of finding positive control invariant sets (PCIS). However, this approach limits the planning horizon of the motion planner since the PCIS must lie completely in the limited...
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