Giovanni L. Santosuosso

Brief Robust adaptive compensation of biased sinusoidal disturbances with unknown frequency

Asymptotically stable, observable linear systems of order n which are not required to be minimum phase and are affected by an additive noisy biased sinusoidal disturbance with unknown bias, magnitude, phase and frequency are considered. The problem of designing an output feedback compensator which regulates the output to zero for any initial condition and for any biased sinusoidal disturbance with no noise is addressed, under the assumption that the system parameters are known. This problem is solved by a (2n+6)-order compensator which generates asymptotically convergent estimates of the biased sinusoidal disturbance and of its parameters, including frequency. The robustness of the closed loop system with respect to sufficiently small additive unmodelled noise is characterized in terms of input-to-state stability.

Global compensation of unknown sinusoidal disturbances for a class of nonlinear nonminimum phase systems

A class of output feedback stabilizable nonlinear systems with known output dependent nonlinearities and affected by unknown sinusoidal disturbances is considered: Nonminimum phase systems are also allowed. The problem of designing a global output feedback compensator which drives the state of the system exponentially to zero is solved when the disturbance consists of a known number of biased sinusoids with any unknown bias, magnitudes, phases, and frequencies.

Unmanned Aerial Vehicle Speed Estimation via Nonlinear Adaptive Observers

In this paper the problem of the speed estimation of an unmanned aerial vehicle is addressed, when acceleration, the angles and the angular speeds are available for measurement. We focus our analysis on a prototype drone - a 4 rotors helicopter robot- which is not equipped with GPS related devices and relies on the inertial measurement unit (IMU) only. A global exponential solution to this open problem is provided in the framework of adaptive observation theory when exact measurements are available. A modified estimator is presented to enhance robustness in velocity estimation in the realistic case of noisy acceleration measurements.

Regulation of Linear Systems With Unknown Exosystems of Uncertain Order

The problem of designing an output feedback control law which exponentially achieves output regulation is considered for known stabilizable and detectable linear systems which are allowed to be non-minimum phase; output references and/or additive disturbances are both generated by a linear exosystem with unknown purely imaginary eigenvalues and uncertain order. The novelty of this note is to require only an upper bound on the exosystem order to achieve a global solution which includes exponentially convergent estimates of the exosystem unknown frequencies

Regulation of Linear Systems with Unknown Additive Sinusoidal Sensor Disturbances

Known linear stabilizable and detectable systems, which are allowed to be non minimum phase, are considered: the problem of tracking unknown output reference trajectories and rejecting unknown input disturbances when the output tracking error is affected by unknown additive sensor disturbances is addressed. All the exogenous signals to be tracked and/or to be rejected are assumed to be the sum of sinusoids: only upper bounds on their numbers are supposed to be known, along with a set in which the output disturbance frequencies may range. A constructive algorithm is proposed to drive the regulation error exponentially to zero. The regulation strategy includes an on-line detector of the number of excited frequencies and exponentially converging estimates of the exosystems parameters. An example containing a variable number of frequencies is worked out and simulated.

Output Feedback Stabilization of Linear Systems with Unknown Additive Output Sinusoidal Disturbances

The output feedback exponential stabilization problem is addressed for known linear stabilizable and detectable systems when the measured output is affected by sinusoidal disturbances generated by an unknown exosystem and only an upper bound on the exosystem order is supposed to be known.Necessary and sufficient conditions are given: in particular a solution to the problem exists if and only if the set of exosystem eigenvalues is disjoint from the set of system eigenvalues. Two adaptively stabilizing control algorithms are proposed: the first one drives the state of the given system exponentially to zero when the actual disturbances are exactly modelled by the exosystem. When the exosystem overmodels the actual disturbances an on-line detector of the number of excited frequencies is included in the second more complex algorithm: the exponentially converging estimates of the system state variables are then used to drive the state of the given system exponentially to zero. An illustrative example with a disturbance containing a variable number of frequencies is worked out in details and simulated.

On the linear regulator with unknown stable exosystems

Given a stabilizable and detectable linear system with additive disturbances and output references generated by a linear exosystem with unknown parameters and unknown order, the problem of designing a global output feedback regulator which asymptotically achieves output regulation and disturbance rejection is considered. The linear system to be regulated is allowed to be a non-minimum phase: its parameters are required to be known. Only an upper bound on the number of the excited frequencies of the exosystem is assumed to be known. A global solution is proposed, which includes asymptotically convergent estimates of the excited unknown frequencies.

Global exponential regulation of discrete time linear systems with unknown neutrally stable exosystems

Discrete time, linear, stabilizable and detectable systems with known parameters are considered: the regulation problem is addressed when the reference output and/or the disturbances contain sinusoidal terms generated by a linear exosystem with unknown parameters. Only an upper bound on the number of unknown sinusoids is supposed to be known. A constructive algorithm is proposed to drive the regulation error exponentially to zero on the basis of its measurement only, under the same necessary and sufficient conditions which are required when the exosystem is known. The control strategy includes an online detector for the number of excited frequencies and exponentially converging global estimates of the exosystem unknown parameters. An illustrative example containing a variable number of frequencies is worked out and simulated.

Adaptive Observer and Kalman Filtering

Abstract In this paper the problem of the speed estimation of an Unmanned Aerial Vehicle is addressed, when only the standard outputs (acceleration, angles and angular speeds) are available for measurement. We focus our analysis on a prototype drone - a 4 rotors helicopter robot-which is not equipped with GPS related devices and relies on the Inertial Measurement Unit (IMU) only. Two different approaches have been compared. The first one uses a classical method based on Kalman Filtering while the second solution is provided in the frame of adaptive observation theory. These estimators have been tested in two situations : when exact measurements are available and in the more realistic case of noisy acceleration measurements.

Two Global Regulators for Systems with Measurable Nonlinearities and Unknown Sinusoidal Disturbances

Summary. The class of nonlinear observable systems with known output dependent nonlinearities affected by disturbances generated by an unknown linear exosystem is considered. The output feedback set point regulation problem is addressed by adaptively generating the reference input on line when the exosystem is unknown. Two global solutions to this problem are provided, when only an upper bound on the exosystem order is known: the first one is simpler but is restricted to minimum phase systems while the second one can handle non-minimum phase systems as well and identify the exosystem parameters.