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This work proposes a flatness-based trajectory planning for a quadrotor Unmanned Aerial Vehicle (UAV) system. The objective is to drive the system as fast as possible from an initial position to a final position without violating system constraints. These constraints can be the actuator limits or the maximal allowable pitch and roll angles. By deriving the extrema of the nominal control inputs to...
In this paper we describe and analyze a biochemical network that admits oscillatory solutions. Such network simplifies and generalizes the chemical reaction structure of a recently published synthetic in vitro oscillator [1]. We analytically demonstrate that this system admits oscillatory solutions, using simple linearization techniques. Numerical simulations suggest that the oscillatory domain of...
Obtaining the Puiseux Series expansion of multiple imaginary (characteristic) roots (MIRs) is a fundamental issue in the stability analysis of time-delay systems. However, this issue has not been fully investigated up to date. This work focuses on the Puiseux Series expansion of MIRs for a class of linear time-delay systems including commensurate delays. For an MIR of any multiplicity, we propose...
This paper shows how to find lower bounds on, and sometimes solve globally, a large class of nonlinear optimal control problems with impulsive controls using semi-definite programming (SDP). This is done by relaxing an optimal control problem into a measure differential problem. The manipulation of the measures by their moments reduces the problem to a convergent series of standard linear matrix inequality...
In this article, we address an active disturbance rejection controller design for the output reference trajectory tracking problem in a 3 degree of freedom (DOF) Delta Robot. The proposed method relies on purely linear high gain disturbance observation and linear feedback control techniques. The estimation tasks are carried out with the help of Generalized Proportional Integral (GPI) observers, endowed...
This paper describes recent progress in the study of switching linear systems, i.e. linear systems that can be modeled as a family of subsystems connected by switching between a number of discrete modes. We address the problem of stabilization and tracking for switching linear systems in case where the plant switching sequence is unknown. The proposed scheme consists of switching between pre-designed...
A fast implementation of a given predictive controller for nonlinear systems is introduced through a piecewise constant approximate function defined over an hyper-cube partition of the system state space. Such a state partition is obtained by maximizing the hyper-cube volumes in order to guarantee, besides stability, an a priori fixed trajectory error as well as input and state constraints satisfaction...
Despite the pervasiveness of sum of squares (sos) techniques in Lyapunov analysis of dynamical systems, the converse question of whether sos Lyapunov functions exist whenever polynomial Lyapunov functions exist has remained elusive. In this paper, we first show via an explicit counterexample that if the degree of the polynomial Lyapunov function is fixed, then sos programming can fail to find a valid...
Control is traditionally applied using periodic sensing and actuation. In some applications, it is beneficial to use instead event based control, to communicate or make a change only when necessary. There are no known general closed form solutions to such event based control problems. We consider stationary event-based control problems with mixed continuous/discrete time dynamics and stochastic disturbances...
In this paper we construct high-order approximate solutions to the value function and optimal control for a finite-horizon optimal control problem for time-varying discrete-time nonlinear systems. The method consists in expanding the dynamic programming equations (DPE) in a power series, collecting homogeneous polynomial terms and solving for the unknown coefficients from the known and previously...
This paper deals with the observer problem for dynamical systems in a behavioral context. We are given a dynamical system together with a partition of the system variables into a set of known or measured variables and a set of unknown, to be estimated variables. The observer problem is to find a system that produces an estimate of the unknown variables on the basis of the known or measured variables...
An approximation to the SDRE control law for the non-linear benchmark problem is developed, which is a solution of an optimal control problem. Although the SDRE solution of the non-linear benchmark problem was derived using the tools of optimal control, the SDRE control law is not the solution of any optimal control problem. The new control law is obtained by approximating the existing SDRE control...
Nonlinear constrained optimal trajectory control is an important and fundamental area of research that continues to advance. This paper proposes an improved version of the bio-inspired virtual motion camouflage (VMC) method, which is based on the natural phenomenon of motion camouflage. Currently, the VMC method offers fast solutions that fall close to the optimal solution, but the solution optimality...
We give a new convenient parametrization of linear controllers that solve the problem of signal invariance (or disturbance cancellation) for MIMO plants. As an example of application of the obtained results we consider the trajectory tracking problem for non-holonomic wheeled transport robots.
In this paper we study switched systems from a behavioral point of view. We define a switched behavioral system in terms of a bank of behaviors without referring to the notion of state. Moreover we give sufficient conditions for the stability of a switched behavior in terms of the behaviors in the underlying bank.
We develop the formal series technique for analysis of the time-optimal control problem. We introduce a concept of equivalence of symmetric control systems in the sense of time optimality. Our approach is based on the consideration of a free algebra of iterated integrals and structures induced in this algebra by control systems. It is close to a homogeneous approximation problem and, in essence, yields...
We give a simple, explicit example of a two-dimensional polynomial vector field that is globally asymptotically stable but does not admit a polynomial Lyapunov function.
In this paper we study solutions to linear ordinary constant coefficient differential equations on the half-line and relate impulsive solutions to the pole/zero structure at infinity of an associated polynomial matrix. While this relation has been thoroughly studied for first order systems, and through first order analysis also for higher order systems partially, the use of the ‘state map’, in particular...
In optimal control, the input trajectories are often solved numerically or analytically. This requires that all variables which enter the optimality conditions are known or measured. We use techniques from polynomial elimination theory to eliminate variables which are not known from the optimality conditions. The result is an expression of the optimality conditions in known variables only, which can...
This paper proposes a novel trajectory generation method considering physical system limitations such as maximum velocity, acceleration, and jerk. Also, the trajectory generation method uses a digital convolution for reducing computational load in robotic motion applications. The method to be proposed has several advantages; first, a continuously differentiable trajectory is simply obtained by applying...
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