Joel Perez

Optimal filtering for polynomial system states with polynomial multiplicative noise

In this paper, the optimal filtering problem for polynomial system states with polynomial multiplicative noise over linear observations is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and the error variance. As a result, the Ito differentials for the optimal estimate and error variance corresponding to the stated filtering problem are first derived. The procedure for obtaining a closed system of the filtering equations for any polynomial state with polynomial multiplicative noise over linear observations is then established, which yields the explicit closed form of the filtering equations in the particular cases of of a linear state equation with linear multiplicative noise and a bilinear state equation with bilinear multiplicative noise. In the example, performance of the designed optimal filter is verified for a quadratic state with a quadratic multiplicative noise over linear observations against the optimal filter for a quadratic state with a state-independent noise and a conventional extended Kalman-Bucy filter.

Analysis via Passivity Theory of a Class of Nonlinear PID Global Regulators for Robot Manipulators

We present a simple global asymptotic stability analysis, by using passivity theory for a class of nonlinear PID regulators for robot manipulators. Nonlinear control structures based on the classical PID controller, which assure global asymptotic stability of the closed-loop system, have emerged. Some works that deal with global nonlinear PID regulators based on Lyapunov theory have been reported by (Arimoto, 1995a), (Kelly, 1998) and (Santibanez & Kelly, 1998). Recently, a particular case of the class of nonlinear PID global regulators originally proposed in (Santibanez & Kelly, 1998) was presented by (Sun et al., 2009). Few saturated PID controllers (that is, bounded PID controllers taking into account the actuator torque constraints) have been reported: for the case of semiglobal asymptotic stability, a saturated linear PID controller was presented in (Alvarez et al., 2003) and (Alvarez et al., 2008); for the case of global asymptotic stability, saturated nonlinear PID controllers were introduced in (Gorez, 1999), (Meza et al., 2005), (Santibanez et al., 2008). The work introduced by (Gorez, 1999) was the first bounded PID-like controller in assuring global regulation; the latter works, introduced in (Meza et al., 2005) and (Santibanez et al., 2008), also guarantee global regulation, but with the advantage of a controller structure which is simpler than that presented in (Gorez, 1999). A local adaptive bounded regulator was presented by (Laib, 2000). Recently a new saturated nonlinear PID regulator for robots has been proposed in (Santibanez et al., 2010), the controller structure considers the saturation phenomena of the control computer, the velocity servo-drivers and the torque constraints of the actuators. The work in (Orrante et al., 2010) presents a variant of the work presented by (Santibanez et al., 2010), where now the controller is composed by a saturated velocity proportional (P) inner loop, provided by the servo-driver, and a saturated position proportional-integral (PI) outer loop, supplied by the control computer. In this chapter we use a passivity based approach to explain the results of global regulation of a class of nonlinear PID controllers proposed by (Santibanez & Kelly, 1998), that include the particular cases reported by (Arimoto, 1995a) and (Kelly, 1998). At the end of the 80’s, it was established in (Kelly & Ortega, 1988) and (Landau & Horowitz, 1988) that the nonlinear Analysis via Passivity Theory of a Class of Nonlinear PID Global Regulators for Robot Manipulators

Stabilization of stochastic recurrent neural networks via inverse optimal control

The paper studies the stabilization problem for a dynamic neural network disturbed by additive noise. The stabilization is achieved from the inverse optimal control approach, introduced in nonlinear control theory, using a quadratic Lyapunov function. A simple feedback control law is derived, which ensures that the neural network state is globally asymptotically stable in probability.

Chaos synchronization via adaptive recurrent neural control

This paper proposes a new adaptive control structure, based on a dynamic neural network, for trajectory tracking of unknown nonlinear plants. The main components of this structure include a neural identifier and a control law, which together guarantee the desired trajectory tracking performance. Stability of the tracking control is analyzed by using the Lyapunov function method, and the structure is tested by simulations on an example of complex dynamical systems: chaos synchronization.

Optimal Filtering for Linear System States over Polynomial Observations

In this paper, the optimal filtering problem for linear system states over polynomial observations is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and the error variance. As a result, the Ito differentials for the optimal estimate and error variance corresponding to the stated filtering problem are first derived. The procedure for obtaining a closed system of the filtering equations for a linear state over observations with any polynomial drift is then established. In the example, the obtained optimal filter is applied to solution of the optimal third order sensor filtering problem, assuming a Gaussian initial condition for the third order state. The resulting filter yields a reliable and rapidly converging estimate

Trajectory tracking for delayed recurrent neural networks

This paper deals with the problem of trajectory tracking for delayed recurrent neural networks. The tracking error is global asymptotic stabilized by a control law derived on the basis of a Lyapunov-Krasovsky functional. Then, it is established that this control law minimizes a meaningful cost functional. Applicability of the approach is illustrated by means of an example

Sequence conservation of the 12D3 gene in Mexican isolates of Babesia bovis.

The 12D3 antigen present in Babesia bovis has been evaluated as a recombinant vaccine candidate and the 12d3 coding sequence has been reported for an Australian and an USA (Texas) isolate of B. bovis. However, no approach has been conducted to perform analysis of 12d3 sequence conservation on a larger number of B. bovis isolates. This could provide important information to determine whether a recombinant vaccine containing this antigen could be widely used. This study reports the cloning and sequencing analysis of the 12d3 coding region in 20 different B. bovis isolates collected from various geographical regions in the tropics and subtropics of Mexico. Comparative analysis of the consensus nucleotide sequences obtained for each isolate revealed a high degree of conservation (94-99% sequence identity) among the 12d3 alleles present in the Mexican isolates when compared with the 12d3 ORF sequences from the Texan (T2Bo) B. bovis isolate. Similarly, BLASTX sequence homology search showed a high percent identity (93-99%) of the deduced amino acid 12D3 sequence as compared with the T2Bo isolate sequence. The high level of sequence conservation in 12d3 among the 20 B. bovis isolates collected from geographically distant locations in Mexico suggests that there exists a minimal bovine-host immunological pressure which could be translated into antigenic diversity or variation, and most probably this is reflected in the non-inmunodominant characteristic of the 12D3 antigen as it has been previously described in the literature. 12D3 antigen can be considered as a viable candidate for inclusion in a recombinant vaccine for cattle babesiosis caused by B. bovis in Mexico.

Optimal Filtering for Polynomial Systems with Partially Measured States and Multiplicative Noises

In this paper, the optimal filtering problem for polynomial systems with partially measured linear part and polynomial multiplicative noise over linear observations is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and the error variance. As a result, the Ito differentials for the optimal estimate and error variance corresponding to the stated filtering problem are first derived. The procedure for obtaining a closed system of the filtering equations for any polynomial state with partially measured linear part and polynomial multiplicative noise over linear observations is then established, which yields the explicit closed form of the filtering equations in the particular case of a bilinear system state with bilinear multiplicative noise. In the example, the designed optimal filter is applied to solution of the optimal cubic sensor filtering problem, assuming a Gaussian initial condition for the cubic state. The resulting filter yields a reliable and rapidly converging estimate

Optimal filtering for linear states over polynomial observations

In this paper, the optimal filtering problem for linear system states over polynomial observations is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and the error variance. As a result, the Ito differentials for the optimal estimate and error variance corresponding to the stated filtering problem are first derived. The procedure for obtaining a closed system of the filtering equations for a linear state over observations with any polynomial drift is then established. In the example, the obtained optimal filter is applied to solution of the optimal third order sensor filtering problem, assuming a conditionally Gaussian initial condition for the third degree state. This assumption is quite admissible in the filtering framework, since the real distributions of the first and third degree states are actually unknown. The resulting filter yields a reliable and rapidly converging estimate.

Stabilization of delayed neural networks

Stability analysis of delayed neural networks has been extensively developed recently. As a continuation of their previous results, in this paper, the authors propose a new methodology for the stabilization of such networks. The approach is based on the inverse optima control technique, which has been introduced to nonlinear system in the last decade of the twentieth century. An example is included to illustrate the applicability of the proposed approach.